How Stueckelberg Extends the Standard Model and the MSSM
δAµ = ∂µ ǫ ,
δσ = −mǫ .
The resulting Lagrangian is gauge invariant and renormalizable3,4. The physical spectrum contains just the massive vector field, and this mass growth occurs without the need for a charged scalar field developing a vacuum expectation value, without spontaneous symmetry breaking and accordingly without the need for a Higgs potential. In the above the mass parameter m is called a topological mass4 . One can now go through the procedure of gauge fixing, so that Aµ and σ decouple in the final theory, m2 1 1 m2 2 1 Aµ Aµ − (∂µ Aµ )2 − ∂µ σ∂ µ σ − ξ σ . LSt + Lgf = − Fµν F µν − 4 2 2ξ 2 2 A number of properties of this Lagrangian should be stressed. i) The vector Aµ has absorbed the real scalar σ in the process of getting a mass, with nothing left. ii) As the global subgroup of the gauge transformation, one can shift the scalar by a constant, δσ = c. This is a Peccei-Quinn like shift symmetry, and is the reason why we call σ an axionic pseudoscalar, which only appears with derivative couplings.a iii) Currently it appears possible to write such a gauge invariant Stueckelberg Lagrangian only for an abelian gauge symmetry, not for non-abelian gauge transformations3. However, as will become clearer from the string theoretic embedding of the Stueckelberg mechanism into D-brane models, the relevant U (1) gauge group can become a subgroup of some non-abelian and simple grand unified gauge group in higher dimensions. 2. Stueckelberg couplings in string theory and supergravity One immediate way to see that Stueckelberg couplings appear in dimensional reduction of supergravity from higher dimensions, and in particular string theory, is to consider the reduction of the ten-dimensional N = 1 supergravity coupled to supersymmetric Yang-Mills gauge fields, in the presence of internal gauge fluxes. The ten-dimensional kinetic term for the anti-symmetric 2-tensor BIJ involves a coupling to the Yang-Mills ChernSimons form, schematically ∂[I BJK ] + A[I FJK ] + · · · , in proper units. Dia But σ does not necessarily have to couple to the QCD gauge fields in the usual topological term. In fact, we assume such couplings to be absent.
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1 gauge invariant. To achieve this, one replaces Aµ −→ Aµ + m ∂µ σ , where σ is an axionic scalar that takes the role of the longitudinal mode of the massive vector, and defines the gauge transformation
¨ BORIS KORS Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA kors@ PRAN NATH Department of Physics, Northeastern University, Boston, MA 02115, USA nath@
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HOW STUECKELBERG EXTENDS THE STANDARD MODEL AND THE MSSM
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mensional reduction with a vacuum expectation value for the internal gauge field strength, Fij = 0, leads to ∂µ Bij + Aµ Fij + · · · ∼ ∂µ σ + mAµ , after identifying the internal components Bij with the scalar σ and the value of the gauge field strength with the mass parameter m, which is indeed a topologiucal quantity, related to the Chern numbers of the gauge bundle. Thus Aµ and σ have a Stueckelberg coupling of the form Aµ ∂ µ σ . These couplings play an important role in the Green-Schwarz anomaly cancelation mechanism. In the effective four-dimenional theory, for instance abelian factors in the gauge group can have an anomalous matter spectrum, whose ABJ anomaly is canceled by Green-Schwarz type contributions. These in˜ µν in the Lagrangian. volve the two terms mAµ ∂µ σ + c σFµν F σ
Abelian vector bosons can get massive through the Stueckelberg mechanism without spontaneous symmetry breaking via condensation of Higgs scalar fields. This appears very naturally in models derived from string theory and supergravity. The simplest scenarios of this type consist of extensions of the Standard Model (SM) or the minimal supersymmetric standard model (MSSM) by an extra U (1)X gauge group with Stueckelberg type couplings. For the SM, the physical spectrum is extended by a massive neutral gauge boson Z′ only, while the extension of the MSSM contains a CP-even neutral scalar and two extra neutralinos. The new gauge boson Z′ can be very light compared to other models with U (1)′ extensions. Among the new features of the Stueckelberg extension of the MSSM, the most striking is the possibility of a new lightest supersymmetric particle (LSP) χ ˜0 St which is mostly composed of Stueckelberg fermions. In this scenario the LSP of the MSSM χ ˜0 1 is . Such decays alter the signatures of supersymmeunstable and decays into χ ˜0 St try and have impact on searches for supersymmetry in accelerator experiments. Further, with R-parity invariance, χ ˜0 St is the new candidate for dark matter.
大学英语六级07-12阅读理解和答案解析
2007年6月Y ou hear the refrain all the time: the U.S. economy looks good statistically, but it doesn’t feel good. Why doesn’t ever-greater wealth promote ever-greater happiness? It is a question that dates at least to the appearance in 1958 of The Affluent (富裕的)52. What question does John Kenneth Galbraith raise in his book The Affluent Society? BB) Why affluence doesn’t guarantee happiness.53. According to Galbraith, people feel discontented because __D__.D) materialism has run wild in modern society54. Why do people feel squeezed when their average income rises considerably? AA) Their material pursuits have gone far ahead of their earnings.55. What does Louis Uchitelle mean by “the disposable American” (Line 3, Para. 5)?DD) Workers who no longer have secure jobs.56. What has affluence brought to American society? CC) New conflicts and complaints.Questions 57 to 61 are based on the following passage.The use of deferential (敬重的) language is symbolic of the Confucian ideal of the woman, which dominates conservative gender norms in Japan.57. The first paragraph describes in detail ____B____.B) the Confucian influence on gender norms in Japan58. What change has been observed in today’s young Japanese women?BB) The use fewer of the deferential linguistic forms.59. How do some people react to women’s appropriation of men’s language forms as reported in the Japanese media? DD) They express strong disapproval.60. According to Y oshiko Matsumoto, the linguistic behavior observed in today’s young women _____B___.B) has been true of all past generations61. The author believes that the use of assertive language by young Japanese women is_____C___.C) one of their strategies to compete in a male-dominated society2007年12月Like most people, I’ve long understood that I will be judged by my occupation, that my profession is a gauge people use to see how smart or talented I am.52. The author was disappointed to find that ___________________.C) one’s occupation affects the way one is treated as a person53. What does the author intend to say by the example in the second paragraph?A) Some customers simply show no respect to those who serve them.54. How did the author feel when waiting tables at the age of 19?D) She found it natural for professionals to treat her as inferior.55. What does the author imply by saying “…many of my customers didn’t get the difference between server and servant” (Lines 3-4, Para.7)?B) Those working in th e service industry shouldn’t be treated as servants.56. The author says she’ll one day take her clients to dinner in order to _______.A) see what kind of person they arePassage TwoWhat’s hot for 2007 among the very rich? A S7.3 million diamond ring. A trip to Tanzania to hunt wild animals. Oh. and income inequality.57. What is the current topic of common interest among the very rich in America? CC) The inequality in the distribution of wealth.58. What do we learn from Mortimer Zucker man’s lamentation? CC) The American nation is becoming more and more divided despite its wealth.59. From the fifth paragraph we can learn that ______B______.B) the very rich are politically sensitive60. What is the real reason for plutocrats to express solidarity with the middle class? CC) They want to gain support for global economic integration.61. What may happen if the United States places obstacles in the way of foreign investors and foreign goods? DD) Foreign countries will place the same economic barriers in return.2008年6月Imagine waking up and finding the value of your assets has been halved. No, you’re not an investor in one of those hedge funds that failed completely.52. Why do Americans feel humiliated? CC) Their currency has slumped53.How does the current dollar affect the life of ordinary Americans? CC) They have to spend more money when buying imported goods.54 How do many Europeans feel about the U.S with the devalued dollar? DD) They think of it as a good tourist destination.55 what is the author’s advice to Americans? CC)They vacation at home rather than abroad56 What does the author imply by saying “currencies don’t turn on a dime” (Line 2,Para 7)? AA)The dollar’s value will not increase in the short term.Passage TwoIn the college-admissions wars, we parents are the true fights. We are pushing our kids to get good grades, take SA T preparatory courses and build resumes so they can get into the college of our first choice.57.Why dose the author say that parents are the true fighters in the college-admissions wars? DD.they care more about which college their children go to than the children themselves.58.Why do parents urge their children to apply to more school than ever?AA.they want to increase their children chances of entering a prestigious college.59.What does the author mean by kids count more than their college(Line1,para.4? CC.Kids actual abilities are more importang than their college background.60.What does Krueger study tell us? BB.Degrees of prestigious universities do not guarantee entry to graduate programs.61.One possible result of pushing children into elite universities is that__C____C.they experience more job dissatisfaction after graduation2008年12月Sustainable development is applied to just about everything from energy to clean water and economic growth,52. How do people often measure progress in agriculture? B[B] By its sustainability.53. Specialization and the effort to increase yields have resulted in __D______.[D] the decrease of biodiversity54. What does the author think of traditional farming practices? C[C] They are not necessarily sustainable.55. What will agriculture be like in the 21st century? A[A] It will go through radical changes.56. What is the author’s purpose in writing this passage? D[D] T o urge people to rethink what sustainable agriculture is.Passage TwoThe percentage of immigrants (including those unlawfully present) in the United States has been creeping upward for years. At 12.6 percent,57. How were immigrants viewed by U.S. Congress in the early days? A[A] They were of inferior races.58. What does the author think of the new immigrants? B[B] They can do just as well as their predecessors.59. What does Edward Tells’ research say about Mexican-Americans? D[D] They may forever remain poor and underachievin g.60. What should be done to help the new immigrants? C[C] Prevent them from being marginalized.61. According to the author, the burning issue concerning immigration is____B___.[B] How to help immigrants to better fit into American society2009年6月For hundreds of millions of years, turtles (海龟) have struggled out of the sea to lay their eggs on sandy beaches,52. We can learn from the first paragraph that ___B_____.B．efforts have been made to protect turtles from dying out53. What does the author mean by “Nature is indifferent to human notions of fairness”(Line 1, Para. 2)? DD．The turtle population has decreased in spite of human protection.54. What constitutes a major threat to the survival of turtles according to Elizabeth Griffin? B B．Unregulated commercial fishing.55. How does global warming affect the survival of turtles? AA．It threatens the sandy beaches on which they lay eggs.56. The last sentence of the passage is meant to _C_______.C．call for effective measures to ensure sea turtles’survivalThere are few more sobering online activities than entering data into college-tuition calculators57. What’s the opinion of economists about going to college? CC．College education is rewarding in spite of the startling costs.58. The two Harvard economists note in their study that, for much of the 20th century,_____D___.D．the gap between the earnings of college and high-school graduates narrowed59. Students who attend an in-state college or university can ____A____.A．save more on tuition60. In this consumerist age, most parents ___D_____.D．consider college education a consumer product61. What is the chief consideration when students choose a college today? BB．A satisfying experience within their budgets.2009年12月份There is nothing like the suggestion of a cancer risk to scare a parent, especially one of the over-educated, eco-conscious type52. What does a recent investigation by USA Today reveal? CC) The air quality around Berkeley’s school campuses is poor.53. What response did USA Today’s report draw? CC) Widespread panic.54. How did parents feel in the face of the experts’ studies? CC) They didn’t know who to believe.55. What is the view of the 2004 report in the journal Pediatrics? DD) Attention should be paid to toxic chemical exposure.56. Of the dangers in everyday life, the author thinks that people have most to fear from_______A___.A) the uncertainCrippling health care bills, long emergency-room waits and the inability to find a primary care physician just scratch the surface of the problems that patients face daily.57. The author’s chief concern about the current U.S. health care system is _ C_________.C) the shrinking primary care resources58. We learn from the passage that people tend to believe that ____D______.D) the more doctors taking care of a patient, the better59. Faced with the government threats to cut reimbursements indiscriminately, primary care physicians have to _________D_ .D) see more patients at the expense of quality60. Why do many new medical graduates refuse to choose primary care as their career? BB) The current system works against primary care.61. What suggestion does the author give in order to provide better health care? AA) Bridge the salary gap between specialists and primary care physicians.2010年6月Only two countries in the advanced world provide no guarantee for paid leave from work to care for a newborn child. Last spring one of the two, Australia,52. What do we learn about paid family leave from the first paragraph? AA) America is now the only developed country without the policy.53. What has prevented the passing of work-family balance laws in the United States? DD) The opposition from business circles.54. What is Professor Anne Alstott's argument for parental support? BB) Good parenting benefits society.55. What does the author think of America's large body of family laws governing children'sB) The fail to provide enough support for parents56. Why does the author object to classifying parenting as a personal choice? DD) It is basically a social undertaking.A new study from the Center for Information and Research on Civic Learning and Engagement (CIRCLE)57. What is the finding of a new study by CIRCLE? AA) More young voters are going to the polls than before.58. What is a main concern of the writers of Generation O? CC) Whether young people will continue to support Obama's policy.59. What will the Generation O bloggers write about in their posts? DD) Their lives in relation to Obama's presidency.60. What accounts for the younger generation's political strength according to Professor Henry CC) Their utilization of the Internet.61. What can we infer from the passage about Generation X? DD) They are indifferent to politics.2010年12月In the early 20th century, few things were more appealing than the promise of scientific knowledge. In a world struggling with rapid industrialization,52. In the early 20th century Americans believed science and technology could _______.[A] solve virtually all existing problems53. Why did many American scholars become enthusiastic about humanistic studies after World[D] They realized science and technology alone were no guarantee for a better world.54. Why are American scholars worried about education today?[C] America is lagging behind in the STEM disciplines.55. What accounts for the significant decline in humanistic studies today?[A] Insufficient funding.56. Why does the author attach so much importance to humanistic studies?[C] Humanistic thinking helps define our culture and values.Will there ever be another Einstein? This is the undercurrent of conversation at Einstein memorial meetings throughout the year.57. What do scientists seem to agree upon, judging from the first two paragraphs?[B] It will take another Einstein to build a unified theory.58. What was critical to Einstein’s success?[B] His independent and abstract thinking.59. What does the author tell us about physicists today?[D] They often go into fields yielding greater financial benefits.60. What does Brian Greene imply by saying “... it would be a lot harder for him to be heard”[C] Papers like Einstein’s would unlikely get published today.61. When he submitted his papers in 1905, Einstein _______.[B] was little known in academic circles2011年6月Minority Report1. What is the author's main concern about American higher education?B) The low graduation rates of minority students.2. What was the pride of President Barry Mills of Bowdoin College?D) Its increased enrollment of minority students.3. What is the risk facing America?B) The rising generation will be less well educated than the previous one.4. How many African-American students earned their degrees in California community colleges according to a recent review?C) Fifteen percent5. Harvard, Yale, and Princeton show almost no gap between black and white graduation rates mainly because .B) they recruit the best students6. How does Amy Wilkins of the Education Trust view minority students' failure to get a degree?A) Universities are to blame.7. Why do some students drop out after a year or two according to the author?B) They cannot afford the high tuition.Passage OneAt the heart of the debate over illegal immigration lies one key question: are immigrants good or bad for the economy? The American public overwhelmingly thinks they're bad. Yet the consensus among most economists is that immigration, both legal and illegal, provides a small net boost to the economy.52. What can we learn from the first paragraph?D) The general public thinks differently from most economists on the impact of immigration.53. In what way does the author think ordinary Americans benefit from immigration?B) They can get consumer goods at lower prices.54. Why do native low-skilled workers suffer most from illegal immigration?C) They have a harder time getting a job with decent pay.55. What is the chief concern of native high-skilled, better-educated employees about the inflow of immigrants?D) It may place a great strain on the state budget.56. What is the irony about the debate over immigration?C) People are making too big a fuss about something of small impact.Passage TwoPicture a typical MBA lecture theatre twenty years ago. In it the majority of students will have conformed to the standard model of the time: male, middle class and Western. Walk into a class today, however, and you'll get a completely different impression. For a start, you will now see plenty more women – the University of Pennsylvania's Wharton School, for example, boasts that 40% of its new enrolment is female. You will also see a wide range of ethnic groups and nationals of practically every country.57. What characterises the business school student population of today?A) Greater diversity.58. What is the author's concern about current business school education?B) It will produce business leaders of a uniform style.D) It stresses competition rather than cooperation.59. What aspect of diversity does Valerie Gauthier think is most important?C) Attitude and approach to business.60. What applicants does the author think MBA programmes should consider recruiting?C) Applicants from outside the traditional sectors.61. What does Mannaz say about the current management style?D) It is shifting towards more collaborative models.2011年12月Google's Plan for World's Biggest Online Library: Philanthropy Or Act of Piracy?1. Google claims its plan for the world's biggest online library is _____.D) to promote its core business of searching2. According to Santiago de la Mora, Google's book-scanning project will _____.D) make full use of the power of its search engine3. Opponents of Google Books believe that digitally archiving the world's books should be controlled by _____.A) non-profit organizations4. Google has involved itself in a legal battle as it ignored _____.A) the copyright of authors of out-of-print books5. Google defends its scanning in-copyright books by saying that _____.B) it is willing to compensate the copyright holders6. What do we learn about the class action suit against Google?D) It could lead to more out-of-court settlements of such disputes.7. What remained controversial after the class action suit ended?C) Google's further exploitation of its database.Passage oneWhat's the one word of advice a well-meaning professional would give to a recent college graduate? China"} India! Brazil! How about trade!52. How do pessimists interpret the U.S. trade deficit in June?D) It could lead to slower growth of the national economy.53. What does the author say about the trade data of the past two years?A) It indicates that economic activities in the U.S. have increased.54. Who particularly benefit from the rising volume of trade?C) Producers of agricultural goods and raw materials.55. What is one of the challenges facing the American economy?B) People's reluctance to sp end.56. What is the author's advice to U.S. companies and individuals?C) To increase their market share overseas.Passage twoA recurring criti cism of the UK's university sector i s its perceived weakness in translatingnew knowledge into new products and services.57. What does the author think of UK universities in terms of commercialization?C) They still have a place among the world leaders.58. What does the author say about the national data on UK universities' performance in commercialization?C) It does not reflect the differences among universities.59. We can infer from Paragraph 5 that "policy interventions" (Line 1, Para. 4) refers to _____.D) concentration of resources in a limited numb er of universities60. What does the author suggest research-led universities do?B) Fully utilize their research to benefit all sectors of society.61. How can the university sector play a key role in the UK's economic growth?C) By promoting technology transfer and graduate school education.2012年6月The Three-Y ear Solution1. Why did Hartwick College start three-year degree programs?B) T o cut students’ expenses.2. By quoting Stephen Trachtenberg the author wants to say that .C) college facilities could be put to more effective use3. The author thinks the tenure system in American universities .A)suppresses creative thinking4. What is said about the new three-year degree program at Hartwick?A) Its students have to earn more credits each year.5. What do we learn about Judson College’s three-year degree program?A) It has been running for several decades.6. What changes in high schools help students earn undergraduate degrees in three years?B) More students have Advanced Placement credits.7. What is said to be a drawback of the three-year college program?B) Students don’t have much time to roam intellectually.Passage OneAs anyone who has tried to lose weight knows, realistic goal-setting generally produces the best results. That's partially because it appears people who set realistic goals actually work more efficiently, and exert more effort, to achieve those goals.52. What message does the author try to convey about goal-setting?A) Its negative effects have long been neglected.53. What does Maurice Schweitzer want to show by citing the example of Enron?D) Goals with financial rewards have strong motivational power.54. How did Sears’ goal-setting affect its employees?C) They resorted to unethical practice to meet their sales quota.55. What do advocates of goal-setting think of Schwei tzer’s research?C) Its conclusion is not based on solid scientific evidence.56. What is Schweitzer’s contention against Edwin Locke?D) Studying goal-setting can throw more light on successful business practices.Passage T woFor most of the 20th century, Asia asked itself what it could learn from the modern, innovating West. Now the question must be reversed. What can the West’s overly indebted and sluggish (经济滞长的) nations learn from a flourishing Asia?57. What has contributed to the rapid economic growth in China and India?D) Free market plus government intervention.58. What does Ronald Reagan mean by saying “government is the problem” (line4, Para. 3)?C) Government action is key to solving economic problems.59. What stopped the American economy from collapsing in 2007?D) Effective measures adopted by the government.60. What is the author’s suggestion to the American public in face of the public government deficit?C) They give up the idea of smaller government and less regulation.61. What’s the pr oblem with the European Union?D) Excessive borrowing.。
2015_-_Jian_Geng_-_Thestabilityofboundchloridesincementpastewithsulfa[retrieved_2015-09-23]
![2015_-_Jian_Geng_-_Thestabilityofboundchloridesincementpastewithsulfa[retrieved_2015-09-23]](https://360docs-1393072327.cos.ap-beijing.myqcloud.com/c873140459eef8c75fbfb32d.webp)
The stability of bound chlorides in cement paste with sulfate attackJian Geng a ,b ,⁎,Dave Easterbrook b ,Long-yuan Li b ,Li-wei Mo aa Research Center of Green Building Materials and Waste Resources Reuse,Ningbo Institute of Technology,Zhejiang University,China bSchool of Marine Science and Engineering,University of Plymouth,UKa b s t r a c ta r t i c l e i n f o Article history:Received 10July 2014Accepted 25November 2014Available online 27December 2014Keywords:Sulfate attack (C)Bound chlorides (D)Stability (C)Fly ash (D)Ground granulated blast-furnace slag (D)This paper presents an experimental investigation on the stability of bound chlorides in chloride-contaminated cement pastes with and without FA/GGBS when subjected to Na 2SO 4and MgSO 4attack.It is shown that bound chlorides were released in the chloride-contaminated pastes when exposed to Na 2SO 4or MgSO 4solution.This is mainly attributed to the decomposition of Friedel's salt (FS),where Cl −bound in FS is replaced by SO 42−.How-ever there were fewer released chlorides found in the pastes exposed to MgSO 4solution than in those exposed to Na 2SO 4solution.This is partly due to the low pH in the pore solution and partly due to the blocking effect of brucite on ionic transport caused by MgSO 4.The inclusion of FA/GGBS in concrete can increase the decomposition of FS and thus the release of bound chlorides.However,it also resists the penetration of Na 2SO 4and thus reduces the attack of Na 2SO 4.©2014Elsevier Ltd.All rights reserved.1.IntroductionThe corrosion of reinforcing steel in concrete structures,due to chlo-ride ion contamination,is one of the main reasons for the deterioration of concrete structures.There are two forms of chloride ions in concrete.One is free chlorides and the other is bound chlorides.It is well-known that the corrosion of reinforcing steel is mainly induced by the free chlo-rides,so reducing free chlorides by increasing bound chlorides will be bene ficial to the durability of concrete structures.According to the bind-ing mechanism,chloride ions can be bound through chemical reactions and physical absorption.In the former,chloride ions are mainly bound in Friedel's salt (FS)(3CaO·Al 2O 3·CaCl 2·10H 2O)through hydration reactions between chloride ions,tricalcium aluminate (C 3A)and its hydration products.In the latter,chloride ions are mainly absorbed by calcium silicate hydrate (C –S –H gel).It was reported that the formation of bound chlorides could be affected by a multitude of factors such as the quantity of C 3A in cement,supplementary cementitious materials (SCM),alkalinity of pore solution,Ca/Si and Ca/Al of hydration products,chloride salt type,and service condition of concrete structures [1–5].In summary,the chloride binding capacity of concrete can be improved by using SCM or cement with high C 3A content.However,many researchers have identi fied that the stability of bound chlorides,espe-cially of FS,can be affected by pH,carbonation,and chemical erosion [6–9].Sulfate attack is another problem for the durability of concrete struc-tures.The attack of sodium sulfate (Na 2SO 4)and magnesium sulfate (MgSO 4)on concrete is a common phenomenon.The mechanisms of Na 2SO 4and MgSO 4attack on concrete are different,mainly due to the solubility of phases formed with sodium and magnesium ions [10–12].With regard to Na 2SO 4attack,the deterioration of concrete is attributed to the formation of expansion products such as gypsum (CaSO 4·2H 2O)and secondary ettringite (AFt)(3CaO·Al 2O 3·3CaSO 4·32H 2O)according to the following equations:Ca ðOH Þ2þNa 2SO 4þ2H 2O →CaSO 4·2H 2O þ2NaOHð1Þ3ðCaSO 4·2H 2O Þþ3CaO ·Al 2O 3þ26H 2O →3CaO ·Al 2O 3·3CaSO 4·32H 2Oð2Þ2ðCaSO 4·2H 2O Þþ3CaO ·Al 2O 3·CaSO 4·12H 2O þ16H 2O →3CaO ·Al 2O 3·3CaSO 4·32H 2O :ð3ÞWhereas for MgSO 4attack,the transformation of the cementitious C –S –H gel to the non-cementitious magnesium silicate hydrate mush (M –S –H),which has very little strength,is the main reason for the dete-rioration of concrete,although gypsum and secondary AFt are also formed during the attack.In addition,brucite,i.e.Mg(OH)2,will form when magnesium is present in the pore solution,which has low solubil-ity and could densify the pore system and thus affect the transport ofCement and Concrete Research 68(2015)211–222⁎Corresponding author.E-mail address:gengjian@ (J.Geng)./10.1016/j.cemconres.2014.11.0100008-8846/©2014Elsevier Ltd.All rightsreserved.Contents lists available at ScienceDirectCement and Concrete Researchj o u rn a l h o m e p a g e :h t tp ://e e s.e l s e v i e r.c o m /C EM C O N /d e f a u l t.a s pions in the cement paste.The mechanism of MgSO4attack occurs according to the following equations:CaðOHÞ2þMgSO4þ2H2O→CaSO4·2H2OþMgðOHÞ2ð4Þx CaO·y SiO2·z H2Oþx MgSO4þð3xþ0:5y−zÞH2O→xðCaSO4·2H2OÞþx MgðOHÞ2þ0:5yð2SiO2·H2OÞð5Þ4MgðOHÞ2þSiO2·nH2O→4MgO·SiO2·8:5H2Oþðn−4:5ÞH2O:ð6ÞIn fact,sulfate attack and chloride contamination are often found to coexist in concrete structures which are exposed to marine and saline environments.The effects of the sulfate and chloride on a concrete structure's durability are multifaceted.On the one hand,the existence of sulfate,especially of Na2SO4,inhibits the formation of FS and reduces the quantity of bound chlorides[13–15].On the other hand,the exis-tence of chloride ions is beneficial for the resistance of concrete to Na2SO4and MgSO4attack[15–18].However,Baghabra argued that the effect of chloride ions on MgSO4attack was slight because the trans-formation of cementitious C–S–H gel to non-cementitious M–S–H was not affected by chloride ions[19].Despite the work on the interaction of sulfate and chloride in con-crete mentioned above,there is very little work on the effect of sulfate attack on the stability of bound chlorides in concrete.Brown and Badger investigated the distributions of bound sulfates and chlorides infield concrete cores exposed to mixed NaCl,Na2SO4and MgSO4attack. They found that there was extensive AFt in the absence of a gypsum zone for some concrete cores[20].Xu et al.obtained similar results, i.e.that sulfate attack could lead to the release of bound chlorides[21]. Both studies suggested the transformation of FS to AFt due to sulfate attack,but the mechanism of FS transform to AFt and the stability of bound chlorides absorbed by C–S–H gel under sulfate attack were not discussed in depth.It is well known that the use offly ash(FA)and ground granulated blast-furnace slag(GGBS)in concrete can not only improve the chloride binding capacity of concrete,but also the resistance of concrete to sulfate attack[22,23].Hence,it would be interesting to know how they affect the stability of bound chlorides when the concrete is under sulfate attack.The purpose of this paper is to report the experimental in-vestigation on the stability of bound chlorides in cement paste under Na2SO4and MgSO4attack,and the corresponding influence of FA and GGBS on the stability of bound chlorides.The stability of bound chlorides in cement paste was examined by analyzing the change of a dimensionless index,R cl,which represents the mass ratio of bound chlo-rides to initial total chlorides in the sample after it was exposed to a5% Na2SO4solution or a5%MgSO4solution for28,56or90days.The mech-anisms of the release of bound chlorides are discussed based on the results of X-ray diffraction(XRD),Fourier transform infrared(FT-IR) and differential thermo-gravimetric analysis(DTG).2.Experiment2.1.MaterialsThe materials used in the experiments were Type42.5Ordinary Portland Cement(OPC),grade II FA and GGBS.The chemical composi-tions of OPC,FA and GGBS are listed in Table1.The potential phase com-positions of OPC,calculated from chemical analysis by Bogue,are given in Table2.All other chemical reagents used in the experiments,but not listed in the tables,are analytically pure.2.2.MethodsIn order to reduce the experimental running time but still able to achieve good and representative results,chloride binding was achieved by using0.5mol/L NaCl solution as the mixing water for the casting of samples.The mass ratio of the mixing water to the binder(cement and SCM)was0.5,which was the same for all samples.The influence of single and combined use of FA and GGBS on the stability of bound chlorides was also investigated.The replacement of cement with SCM was30%by weight,and the proportions of FA to GGBS in the combined samples were either1:1or7:3.The detailed mix proportions of the samples tested are listed in Table3.A total of106samples were tested.All samples were of a size of 40mm×40mm×160mm.There were three groups of samples.The first group(2×5×7samples)were cured at a standard curing condi-tion(20±2°C and95%RH)for periods of1,3,7,14,28,56and90days for the investigation of the effect of curing time and SCM on the evolu-tion of bound chlorides in the cement paste.The second group(2×5×3 samples)were examined for the effect of Na2SO4attack on the stability of bound chlorides.In this group,all samples,after the56days standard curing,were dried at a room temperature(20±2°C and60%RH)for 1day.Then,for each sample itsfive surfaces were sealed by paraffin wax and one40mm×40mm surface was left untouched.After then, all samples were immersed in a covered plastic container(575mm ×400mm×275mm)of5%Na2SO4solution for28,56and90days at the standard curing condition(20±2°C and95%RH).The third group(2×1×3samples)were for the samples only with OPC,which were cured as the same as those done in the second group.The only dif-ference is that they were immersed in a similar covered container of5% MgSO4solution for28,56and90days at the standard curing condition (20±2°C and95%RH)for the examination of the effect of MgSO4at-tack on the stability of bound chlorides.The volume of the sulfate solu-tions used in the immersion tests was25L and the storage solutions were not renewed during the immersed tests.In the second and third groups,when the attack time reached28,56, and90days,the samples were dried at room temperature for1day,and then were sliced into four pieces parallel to the exposed surface (starting from the exposed surface)and each piece is one cm thick. Afterwards,each piece was broken into small blocks,which were then immersed in anhydrous ethanol for7days to terminate hydration. These small blocks were ground intofine powder by passing through a sieve of0.15mm mesh aperture size,which was then stored in a des-iccator with silica gel and soda lime at11%RH to minimize carbonation before it was used in the tests for chloride content titration and other material characterization analyses.The initial total chloride content(C t)of the sample cured at the stan-dard curing condition can be calculated based on the mixing water of Table1Chemical composition of main materials(data presented by mass%).SiO2CaO MgO Fe2O3Al2O3SO3Ignition loss OPC19.6760.43 4.56 4.20 5.70 2.30 2.54FA43.10 6.300.247.2638.200.70 2.04GGBS23.5052.80 6.500.7011.80 1.650.78Table2Potential phase composition of OPC(data presented by mass%).Potential phase composition OPCC3S51.58C2S17.77C3A8.01C4AF12.773.91212J.Geng et al./Cement and Concrete Research68(2015)211–2220.5mol/L NaCl solution,which is 8.863mg ·g −1.The free chloride content (C f )was measured using the traditional leaching method according to the standard of Test Code for Hydraulic Concrete (SL352-2006)and the total chloride content (C t )was measured using the acid-soluble method (SL352-2006).In order to analyze the stability of bound chlorides in concrete,the dimensionless index (R cl )was exam-ined,which is de fined as follows,R cl ¼C t −C f %ð7Þwhere 8.863mg.g −1is the initial total chloride content in the sample.X-ray diffraction (XRD)/reference intensity ratio (RIR)analysis and DTG can be used to approximately determine the quantity of FS,AFt and calcium hydroxide (CH)in the samples.XRD/RIR can determine the relative mass relations among different minerals in a sample,which is calculated according to the following equations [24,25]:W i ¼I i =RIR iX i ¼1I i=RIR i ðÞð8ÞW 1þW 2þW 3þ⋯þW l ¼1ð9Þwhere W i is the relative mass of mineral i ,RIR i is the reference intensityratio of mineral i ,which can be collected from the PDF card of the Inter-national Centre for Diffraction Data (ICDD),I i is the integral intensity of the highest peak of mineral i ,which is calculated using X'Pert HighScore Plus ™software,and N is the number of minerals in the sample.XRD/RIR is usually used to determine the quantity of substances in metals because of simple compositions [25].For cement based materials,it is rather complicated to accurately determine the kinds of hydration products,which increases the dif ficulty of the quantitative analysis.However,if the quantity of one of the minerals can be determinedusing other methods,the calculation process of XRD/RIR becomes pared with the FS and AFt,the quantity of CH can be accurately determined using DTG.Therefore,the quantities of the FS and AFt can be calculated by solving the following algebraic equations,m FS :m AFt ¼T 1ð10Þm FSFS þm AFt þm CH ¼T 2ð11Þm AFtm FS þm AFt þm CH ¼T 3ð12Þm CHm FS þm AFt þm CH¼T 4ð13Þwhere m FS ,m AFt and m CH are masses of FS,AFt and CH,respectively,T 1,T 2,T 3and T 4are the mass ratios,which can be calculated from Eqs.(8)and (9).Note that,m CH can be determined by DTG and thus m FS and m AFt can be determined by Eq.(10)plus any one taken from Eqs.(11)–(13).XRD was carried out using the D8Advance instrument of Bruker AXS with a Cu K αradiation generated with 40kV and 30mA.The diffraction spectra were collected in the range of 5–60°(2θ)scale,with a step sizeTable 3Mix proportions (data presented by mass %).Samples OPC FA GGBS w/b a NoteCN 100000.5Exposed to 5%Na 2SO 4solutionCF 703000.5CG 700300.5CF1G17015150.5CF7G3702190.5CM1000.5Exposed to 5%MgSO 4solutionaw/b represents the mass ratio of mixing water (i.e.0.5mol/L NaCl solution)to binder (cement +SCM).Fig.1.Variation of R cl with standard curing time in samples of differentmixes.Fig.2.Values of R cl in the surface layer of the sample at various different sulfate attack times (CM was exposed to MgSO 4,while all the others were exposed to Na 2SO 4).Fig.3.Values of R cl in different layers of the sample after 90days sulfate attack (1st layer is next to the surface and 4th layer is away from the surface.CM was exposed to MgSO 4,while all the others were exposed to Na 2SO 4).213J.Geng et al./Cement and Concrete Research 68(2015)211–222of 0.02°/s.FT-IR was performed for the samples on a Nicolet Nexus 470spectrometer using the KBr pellet technique in the range of 400–4000cm −1.DTG was carried out in a Netzsch TG-209F1thermal an-alyzer,using a heating rate of 20°C/min at the range of 25–1000°C,in N 2atmosphere.3.Stability of bound chlorides 3.1.Standard curing conditionThe variation of R cl during the standard curing time is shown in Fig.1.It can be seen from the figure that R cl in the samples with SCM is higher than that in the sample only with OPC when they have the same curing time,which is more obvious after the curing time exceeds 14days.Up to 28days,the combined use of FA and GGBS results in higher values of R cl in CF1G1and CF7G3than in the samples with only either FA (CF)or GGBS (CG).However,after the 28days standard curing,the R cl value of the samples has an order of CF ≈CF7G3N CF1G1N CG,which increases with the increased proportion of FA to GGBS.The latereffect of FA on chloride binding is mainly due to its slow pozzolanic re-action.The results shown in Fig.1indicate that the inclusion of SCM in concrete can increase the chloride binding capacity and the effect of FA on chloride binding is more signi ficant than that of GGBS.Furthermore,they also show that the R cl values of all samples increase very obviously before 28days but after that there is less change,suggesting that the equilibrium between free and bound chlorides has been reached.3.2.Sulfate attack conditionFig.2shows the expected decrease in R cl of the surface layer of all samples with the sulfate attack,but the rate of the decrease is higher than that was reported [21].The R cl value in the surface layer of sample CN exposed to Na 2SO 4solution,for example,decreases from 59.8%to 4.3%after only 28days.After that,R cl continuously decreases with the attack time but with a slow reduction rate,from 4.3%at 28days to 1.9%at 90days.The results for locations other than the surface layer at 90days are shown in Fig.3.It can be seen from the figure that,although the 4th layer of sample CN is far away from theexposedFig.4.XRD patterns of samples CN(CM),CF and CG at standard curing condition for (A)28and (B)56days (E:ettringite (AFt),F:Friedel's salt (FS),CH:calcium hydroxide,M:mono-sulfoaluminate,V:Vaterite,CSH:C –S –H gel,C:calcite).214J.Geng et al./Cement and Concrete Research 68(2015)211–222surface,there is still a notable decrease in the R cl value from59.8%at the beginning of the Na2SO4attack to16.6%after90days of attack.This demonstrates that the stability of bound chlorides in concrete is very susceptible to Na2SO4attack.Note that the data plotted in Fig.2show that there is also a decrease in the R cl values of the samples with SCM after Na2SO4attack for28days, but the R cl values are still higher than that of the sample CN only with OPC.This suggests that the use of SCM can alleviate the effect of Na2SO4attack on the stability of bound chlorides.This is partly because the effect of SCM on the diffusion of ions,since the ionic diffusion coef-ficient in cement paste with SCM is normally lower than that in OPC paste,and partly because the cement paste with SCM has more bound chlorides[26].Additionally,in contrast with the results obtained under the standard curing condition,the R cl values of the samples with SCM increase with the decreased proportion of FA to GGBS,and also the R cl value of the surface layer of sample CF is the lowest of all samples containing SCM,following the Na2SO4attack.This suggests that Na2SO4attack can also alter the effect of SCM on the stability of bound chlorides.This appears to be consistent with what is reported in literature[21].The stability of bound chlorides in concrete under MgSO4attack is also shown in Figs.2and3.When the MgSO4attack time extends from0to28days,the R cl value of the surface layer of sample CM decreases from59.8%to26.3%,which is slower than that of sample CN exposed to Na2SO4solution.When the attack time reaches90days, the R cl value of sample CM's surface layer decreases to7.5%,which is still almost four times as high as that of sample CN.This indicates that the stability of bound chlorides is less susceptible to MgSO4attack when compared with Na2SO4attack.Again,thisfinding is consistent with what is reported in other experiments[21,27].The different reductions of R cl in samples CM and CN reflect the different effects of MgSO4and Na2SO4on bound chlorides.During the immersion process free chloride ions will diffuse out and sulfate ions will diffuse into the specimen.The former may decrease the bound chlo-ride level in the sample owing to the equilibrium between the free and bound chlorides.The latter can transform FS into AFt,which not only can reduce the bound chlorides but also can change the pore system and thus affect the diffusion rate of ions.In addition,when magnesium is present,brucite will be formed,which can also change the pore sys-tem and thus affect the transport of ions and the R cl value.The slower reduction of R cl found in sample CM shown in Figs.2and3indicates that the magnesium ions must have some influence on the sulfate attack to the bound chlorides.This influence could be physical and/or chemi-cal.The former is mainly due to the forming of brucite in the surface layer,which reduces the inward diffusion of sulfate ions and the out-ward diffusion of chloride ions.Indeed,the measured free chloride con-centration after the90days immersion was found to be higher in sample CM than in sample CN and have the ratios of about1:0.72for the surface layer and1:0.81for the4th layer.An accurate analysis for the diffusion effect on the bound chlorides requires having more data on thinner layers and knowing the binding isotherms.Nevertheless, the above results did indicate that the diffusion of chloride ions was affected by magnesium ions.The chemical effect of magnesium ions on bound chlorides will be discussed in the next section.Note that the ionic diffusion coefficient in concrete with SCM is nor-mally smaller than that in concrete only with OPC.Thus,the inclusion of SCM in cement paste can provide additional resistance to the ingress of sulfate ions,which in turn can affect the stability of bound chlorides. More discussion on this will be provided in the next section.4.Material characterization analyses4.1.X-ray diffractionThe XRD patterns of samples CN,CF and CG cured at the standard curing condition for28and56days are shown in Fig.4.From the XRD patterns one can identify the FS with a very obvious diffraction peak at around11°2θ.Fig.5shows the relative masses of AFt,FS and CH in samples CN,CF and CG after they were cured in the standard condition for56days.It can be seen from thefigure that the use of FA and GGBS is beneficial to forming more FS.This result can be attributed to two rea-sons.First,the forming process of FS in concrete has been associated with the quantity of aluminate in cementious materials.The higher the quantity of aluminate,the more FS is formed.According to the chemical composition shown in Table1,there is a larger quantity of alu-minate in GGBS and FA than in OPC,which can be released due to the latent hydraulic property of GGBS and the pozzolanic property of FA, which is beneficial to the formation of FS.Secondly,the formation of FS would be hindered because SO42−can react with aluminate prior to Cl−to form mono-sulfoaluminate(AFm)and AFt[13–15].In addition, C–A–H and C–S–H gel,formed due to the hydration reactions induced by FA and GGBS,are also beneficial to chloride binding.As shown in Fig.5,although the quantity of aluminate in FA is higher than that in GGBS,the quantity of FS in sample CF is still lower than that in sample CG after standard curing for56days.It was believed that only reactive alumina Al2O3r−in SCM could react with Cl−to form FS[5].The quantity of CaO in FA used in this study is6.3%,which is low calciumfly ash according to Chinese specification GB/T15696-2005,and where Mullite is the main form of Al2O3,so it is adverse to the formation of FS.Nevertheless,a notable decrease in the intensity of diffraction peak (IDP)of CH can be found in the XRD patterns of sample CF over the curing time from28to56days,which is induced due to the pozzolanic reaction between CH and FA.As a result,more C–S–H gel and C–A–H are formed,which could increase the bound chlorides in sample CF.It should be noticed that the IDP change at around30°(2θ)shown in Fig.4correlates with both C–S–H gel and calcite(CaCO3),because of the overlap of the two strongest diffraction peaks at29.25°(2θ)and 29.40°2θ,respectively[8,28].The XRD patterns of sample CN under Na2SO4attack are shown in Fig.6.It can be observed from Fig.6A that the IDP of FS in the surface layer of sample CN becomes very weak after Na2SO4attack for28 days,which indicates that FS has been decomposed due to the Na2SO4 attack.A quantitative analysis of FS,AFt and CH of sample CN after the Na2SO4attack for28and90days is shown in Fig.7.It can be seen from thefigure that the relative mass of FS in the sample decreases very quickly from2.04to0.45after the28days attack.This suggests that the stability of FS is very susceptible to Na2SO4attack,which may also explain why the decrease of R cl is quick as is shown in Fig.2.How-ever,when the attack time is extended from28to90days,the change in the quantity of FS is slight,which indicates that a large quantity of FShasFig.5.Analysis of ettringite(AFt),Friedel's salt(FS)and calcium hydroxide(CH)in sam-ples CN/CM,CF and CG after they had56days standard curing(wt.%represents the mass percentage of AFt/FS/CH in sample).215J.Geng et al./Cement and Concrete Research68(2015)211–222been decomposed following 28days of the Na 2SO 4attack.Moreover,it can be seen from Fig.7that the quantity of FS gradually decreases from the inside to the surface,which correlates with the change of the R cl value shown in Fig.3.In addition,one can see from Fig.6B that AFt with a diffraction peak at around 9°(2θ)can be detected in every layer of sample CN after the Na 2SO 4attack for 90days.The data shown in Fig.7for AFt indicate that the quantity of AFt in the fourth layer of sam-ple CN is higher than its initial value,which con firms that the attack of Na 2SO 4has reached the fourth layer of the sample.Fig.7also shows the expected opposite changes of FS and AFt with time.The XRD patterns of samples CF and CG after the Na 2SO 4attack for 90days are shown in Fig.8.Similar to the sample CN,the diffraction peaks of FS in the samples with SCM,especially in sample CF,become very weak.Similar to the analysis of the sample CN,Fig.9shows the relative mass of FS,AFt and CH of samples CF and CG after the Na 2SO 4attack for 90days.It seems that the quantities of FS in samples CF and CG are as high as that in sample CN after the Na 2SO 4attack.However,considering the higher quantity of FS in samples CF and CG before the Na 2SO 4attack as shown in Fig.5,the decrease of the quantity of FS in them is quicker than that in sample CN.Therefore,it can be concluded that the stability of FS in the samples with FA or GGBS is susceptible to Na 2SO 4attack when compared to the sample CN.The XRD patterns of samples CN and CM attacked by Na 2SO 4and MgSO 4for 90days are shown in Fig.10.An interesting finding is that there is still an obvious diffraction peak of FS in the sample CM,which is different from the sample CN attacked by Na 2SO 4.The analysis results shown in Fig.11demonstrate that there is more FS in sample CM than in sample CN.Therefore,it can be concluded that the Na 2SO 4attack has more effect on the decomposition of FS in hardened cement paste than the MgSO 4attack.In addition,the IDP of AFt in sample CM is lower than that in sample CN due to the different erosion mechanisms.However,there is still an obvious increase in AFt for sample CM from 0to 90days as demonstrated in Figs.5and 11,which indicates that MgSO 4attack can also lead to the formation of secondary AFt.NoteFig.6.XRD patterns of samples CN with Na 2SO 4attack.(A)1st layer at different days and (B)different layers at 90days (E:ettringite (AFt),F:Friedel's salt (FS),CH:calcium hydroxide,M:mono-sulfoaluminate,V:Vaterite,CSH:C –S –H gel,C:calcite).216J.Geng et al./Cement and Concrete Research 68(2015)211–222that,when magnesium is included in the exposure solution,brucite is formed at the expense of calcium hydroxide,which can affect not only the leaching of chloride from the specimen but also the inward trans-port of sulfate from the exposed solution and thus provide the in fluence on the decomposition of FS and the formation of AFt.However,our XRD result did not reveal a signi ficant amount of brucite and/or gypsum in the surface layer.This is probably due to the specimen layer used in the tests being too thick.Both Skaropoulou and Sotiriadis reported their test results in which brucite was detected in XRD patterns,but the IDP of it was very weak when compared to other phases [11,17].However,in other similar experiments brucite was not detected in XRD patterns [27,29,30].This is probably attributed to the consumption of brucite due to the formation of M –S –H as shown in Eqs.(4)–(6)[19].4.2.Fourier transform infrared (FT-IR)Fig.12shows the FT-IR spectra of sample CN after the Na 2SO 4attack for 28and 90days,respectively.The band at around 3640cm −1is due to the stretching vibration of \OH in Ca(OH)2[30],which is very weak in all samples due to Na 2SO 4attack.The presence of carbonate bands at around 1430and 870cm −1indicates that the samples have already absorbed CO 2molecules from the air before they were immersed into sulfate solution [31].The band at around 1110cm −1comes from asym-metric stretching vibration of S –O in SO 42−,which is identi fied as the fingerprint peak of AFt [32,33].As is shown in Fig.12,owing to more secondary AFt being formed,this band becomes stronger from the in-side to the surface over the attack time.The changes in the bands at around 3440and 1650cm −1are due to the stretching vibration of \OH in structural water of hydration products and the bending vibra-tion of \OH in the interlayer water of hydration products [30].The two bands are also related to the formation of secondary AFt,which be-come strong with the increased quantity of secondary AFt.In addition,the band at around 970cm −1comes from asymmetric stretching vibra-tion of Si –O in C –S –H gel [31,34].It can be observed from Fig.12that there is no obvious change in this band over the attack time,which sug-gests that the stability of C –S –H gel is independent of Na 2SO 4attack.With regard to FS,because chloride ions are not absorbed in the range 400–4000cm −1,the bands at around 730,530and 460cm −1,which are due to Al –O vibrations of [Al(OH)6]3−,can be identi fied as the fin-gerprint peaks of FS [35,36].Owing to the decomposition of FS under Na 2SO 4attack,the strength of these bands appears very weak.Fig.13shows the FT-IR spectra of samples CF and CG after the Na 2SO 4attack.There is no obvious band at around 3640cm −1in thespectra due to the consumption of CH induced by hydration reactions of FA and GGBS and sulfate attack.It can be observed from Fig.13that there is an increase in the strength of the band of C –S –H gel at 976cm −1in sample CF over the attack time from 56to 90days.Guerre-ro et al.attributed this to the further activating action on FA due to the increase in alkalinity induced by Na 2SO 4attack [15].Moreover,this re-sult also indicates that the stability of C –S –H gel is independent of Na 2SO 4attack.The difference of the bands at 714,535and 458cm −1be-tween samples CF and CG is slight.Fig.14shows the FT-IR spectra of samples CN and CM after Na 2SO 4and MgSO 4attack for 90days,respectively.It is observed from Fig.14that the strength of the band at around 710cm −1in sample CM is much stronger than that in sample CN.Also there is more FS in sample CM than in sample CN,which agrees with the results shown in Figs.10and 11.Moreover,it can be seen clearly from Fig.14that the strength of the band at around 970cm −1in sample CM is lower than that in sample CN.This is likely attributed to the decomposition of C –S –H gel induced by MgSO 4attack.As a result of that,the bound chlorides absorbed by C –S –H gel are released.A weak band at around 1110cm −1in sample CM due to the attack of MgSO 4can induce the formation of secondary AFt.4.3.Derivative thermo-gravimetric analysis (DTG)The DTG curves of sample CN attacked by Na 2SO 4are shown in Fig.15.There are some notable endothermic peaks in the DTG curves.The peak near 100°C is mainly attributed to the dehydration of C –S –H gel and AFt,which are dif ficult to distinguish because of the overlap of dehydration temperature from 85to 130°C [23].The peak near 160°C is attributed to AFm [23].Besides these,the peaks near 340,450and 710°C are attributed to the dehydration of FS,CH and the decomposi-tion of calcite.The absence of the peak for FS in the DTG curve after the Na 2SO 4attack for 28days shown in Fig.15further demonstrates that the stability of FS is susceptible to Na 2SO 4attack.The change in the peak of AFm,which plays an important role in the formation of sec-ondary AFt during the Na 2SO 4attack,is also consistent with the change of FS.Fig.16shows the DTG curves of samples CF and CG after the Na 2SO 4attack for pared to sample CG,sample CF has a weak strength of the peak for FS,which is consistent with the analysis result shown in Fig.9and the R cl data shown in Fig.2.Fig.17shows similar DTG results of samples CN and CM after Na 2SO 4and MgSO 4attack for 90days.It is noticed from the figure that the strength of the peak for C –S –H gel and AFt in sample CM is far lower than that in sample CN.Ac-cording to the FT-IR results shown in Fig.14,this result further indicates that MgSO 4attack will lead to the decomposition of C –S –H gel,resulting in the release of bound chlorides.5.Discussion5.1.Stability of Friedel's saltSuryavanshi and Swamy reported that a drop in alkalinity of pore so-lution due to carbonation could induce the decomposition of FS [8].Con-versely,Na 2SO 4attack can increase the alkalinity of the pore solution,which has a negative effect on chloride binding [23,27,37].The question now is how Na 2SO 4attack affects the stability of FS.The exchange be-tween Cl −and SO 42−is the main mechanism in the formation of FS,which can be explained by the following reaction [27]:3CaO ·Al 2O 3·CaSO 4·12H 2O ðAFm Þþ2Cl −→3CaO ·Al 2O 3·CaCl 2·10H 2O ðFS ÞþSO 2−4þ2H 2O :ð14ÞEssentially,FS belongs to a phase of the AFm family,which has a complex chemical and structural constitution.A general formula for AFm phase is [Ca 2(Al,Fe)(OH)6]+X·m H 2O,where the bracketsindicateFig.7.Analysis of ettringite (AFt),Friedel's salt (FS)and calcium hydroxide (CH)in sample CN after Na 2SO 4attack for 0,28and 90days (wt.%represents the mass percentage of AFt/FS/CH in sample).217J.Geng et al./Cement and Concrete Research 68(2015)211–222。
全新版第二版综合B4U1
全新版第二版综合B4U4-APart I Listening Comprehension ( 15 minutes )Section ADirections: In this section, you will hear ten statements. Numbers 1 to 6 are based on Text A while the rest are based on Text B. Each statement will be read ONLY ONCE. Listen carefully and decide whether each statement is true or false.1.A) TB) FScript: In 1998 William Browder gave up his American passport to become a British citizen, since his life is now centered in Europe.正确答案：A2.A) TB) FScript: Alex Mandl is also a fervent believer in globalization, but he views himself very differently.正确答案：A3.A) TB) FScript: Despite all that globetrotting, Mandl, 55 years old, still identifies himself as a Canadian.正确答案：B4.A) TB) FScript: Although Browder and Mandl define their nationality differently, both see their identity as a matter of personal choice, not an accident of birth.正确答案：A5.A) TB) FScript: As borders and national identities become more important, some find that threatening and even dangerous.正确答案：B6.A) TB) FScript: Global trade has been around for centuries; the corporations and countries that benefited from it were largely content to treat vast parts of the world as places to mine natural resources or sell finished products.正确答案：A7.A) TB) FScript: Text B contrasts Western skeptics with Eastern enthusiasts for globalization and reflects on the way economic integration can help promote greater political tolerance.正确答案：A8.A) TB) FScript: The developed world is beating a path to China's and India's door — and Chinese and Indian companies, in turn, have started to look overseas for some of their future growth.正确答案：A9.A) TB) FScript: China and India haven’t decided that opening their economies to trade in goods and services is the best way to lift their people out of abject poverty and are now focused simply on how to globalize in the most stable manner.正确答案：B10.A) TB) FScript: India is just beginning to realize that this process of globalization is one where the Indian have an inherent advantage.正确答案：ASection BDirections: In this section, you will hear a passage three times. When the passage is read for the first time, you should listen carefully for its general idea. When the passage is read for the second time, you are required to fill in the blanks with the exact words you have just heard. Finally, when the passage is read for the third time, you should check what you have written.This (11)_________________ wave of globalization has been driven by policies that have opened economies (12)_________________ and internationally. In the years since the (13)_________________ , and especially during the past two decades, many governments have adopted free-market (14)_________________ , vastly increasing their own productive (15)_________________ and creating myriad new opportunities for (16)_________________ and investment. Governments also have (17)_________________ dramatic reductions in barriers to commerce and have established international agreements to promote trade in goods, services, and investment. (18)_________________ new opportunities in foreign markets, corporations have built foreign factories and established production and marketing arrangements with foreign partners. Globalization is deeply controversial, however. Proponents of globalization argue that it allows poor countries and their citizens to develop economically and raise their (19)_________________ , while opponents of globalization claim that the creation of an unfettered international free market has benefited multinational corporations in the Western world at the expense of local enterprises, local cultures, and common people. Resistance to globalization has therefore (20)_________________ both at a popular and at a governmental level as people and governments try to manage the flow of capital, labor, goods, and ideas that constitute the current wave of globalization. To find the right balance between benefits and costs associated with globalization, citizens of all nations need to understand how globalization works and the policy choices facing them and their societies.Script: This current wave of globalization has been driven by policies that have opened economies domestically and internationally. In the years since the Second World War, and especially during the past two decades, many governments have adopted free-market economic systems, vastly increasing their own productive potential and creating myriad new opportunities for international trade and investment. Governments also have negotiated dramatic reductions in barriers to commerce and have established international agreements to promote trade in goods, services, and investment. Taking advantage of new opportunities inforeign markets, corporations have built foreign factories and established production and marketing arrangements with foreign partners. Globalization is deeply controversial, however. Proponents of globalization argue that it allows poor countries and their citizens to develop economically and raise their standards of living, while opponents of globalization claim that the creation of an unfettered international free market has benefited multinational corporations in the Western world at the expense of local enterprises, local cultures, and common people. Resistance to globalization has therefore taken shape both at a popular and at a governmental level as people and governments try to manage the flow of capital, labor, goods, and ideas that constitute the current wave of globalization. To find the right balance between benefits and costs associated with globalization, citizens of all nations need to understand how globalization works and the policy choices facing them and their societies.正确答案：current正确答案：domestically正确答案：Second World War正确答案：economic systems正确答案：potential正确答案：international trade正确答案：negotiated正确答案：Taking advantage of正确答案：standards of living正确答案：taken shapePart II Reading Comprehension ( 25 minutes )Section ADirections: In this section, there is a passage with several blanks. You are required to select one word for each blank from a list of choices given in a word bank following the passage. Read the passage through carefully before making your choices. Each choice in the bank is identified by a letter. You may not use any of the words in the bank more than once.A) define B) strengthen C) accident D) at least E) entitle F) politicians G) annual H) implicationsI) be committed to J) earnest K) increasingly L) witness M) World Economic Forum N) forum O) journalists21. ______________________正确答案：A22. ______________________正确答案：C23. ______________________正确答案：G24. ______________________正确答案：M25. ______________________正确答案：F26. ______________________正确答案：O27. ______________________正确答案：J28. ______________________正确答案：H29. ______________________正确答案：D30. ______________________正确答案：KSection BDirections: There are several passages in this section. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A), B), C) and D). You should decide on the best choice.Passage OneQuestions 31 to 35 are based on the following passage.In such a changing, complex society formerly simple solutions to informational needs become complicated. Many of life's problems which were solved by asking family members, friends or colleagues are beyond the capability of the extended family to resolve. Where to turn for expert information and how to determine which expert advice to accept are questions facing many people today.In addition to this, there is the growing mobility of people since World War Ⅱ. As families move away from their stable community, their friends of many years, their extended family relationships, the informal flow of information is cut off, and with it the confidence that information will be available when needed and will be trustworthy and reliable. The almost unconscious flow of information about the simplest aspects of living can be cut off. Thus, things once learned subconsciously through the casual communications of the extended family must be consciously learned.Adding to societal changes today is an enormous stockpile of information. The individual now has more information available than any other generation, and the task of finding that one piece of information relevant to his or her specific problem is complicated, time-consuming and sometimes even overwhelming.Coupled with the growing quantity of information is the development of technologies which enable the storage and delivery of more information with greater speed to more locations than has ever been possible before. Computer technology makes it possible to store vast amounts of data in machine-readable files, and to program computers to locate specific information. Telecommunications developments enable the sending of messages via television, radio, and very shortly, electronic mail to bombard people with multitudes of messages. Satellites have extended the power of communications to report events at the instant of occurrence. Expertise can be shared worldwide through teleconferencing, and problems in dispute can be settled without the participants leaving their homes and/or jobs to travel to a distant conference site. Technology has facilitated the sharing of information and the storage and delivery of information, thus making more information available to more people.In this world of change and complexity, the need for information is of greatestimportance. Those people who have accurate, reliable up-to-date information to solve the day-to-day problems, the critical problems of their business, social and family life, will survive and succeed. "Knowledge is power" may well be the truest saying and access to information may be the most critical requirement of all people.31.The word "it" (Para. 2) most probably refers to _______.A) the lack of stable communitiesB) the breakdown of informal information channelsC) the increased mobility of familiesD) the growing number of people moving from place to place正确答案：B32.The main problem people may encounter today arises from the fact that _______.A) they have to learn new things consciouslyB) they lack the confidence of securing reliable and trustworthy informationC) they have difficulty obtaining the needed information readilyD) they can hardly carry out casual communications with an extended family正确答案：C33.From the passage we can infer that _______.A) electronic mail will soon play a dominant role in transmitting messagesB) it will become more difficult for people to keep secrets in an information eraC) people will spend less time holding meetings or conferencesD) events will be reported on the spot mainly through satellites正确答案：A34.Technology facilitates _______.A) sharing informationB) storing and sending informationC) providing people with easy access to more informationD) all of the above正确答案：D35.We can learn from the last paragraph that _______.A) it is necessary to obtain as muchB) people should make the best use of the informationC) we should realize the importance of accumulating informationD) it is of vital importance to acquire needed information efficiently正确答案：DPassage TwoQuestions 36 to 40 are based on the following passage.In many ways, today’s business environment has changed qualitatively since the late 1980s. The end of the Cold War radically altered the very nature of the world’s politics and economics. In just a few short years, globalization has started a variety of trends with profound consequences: the opening of markets, true global competition, widespread deregulation (解除政府对……的控制) of industry, and an abundance of accessible capital. We have experienced both the benefits and risks of a truly global economy, with both Wall Street and Main Street (平民百姓) feeling the pains of economic disorder half a world away.At the same time, we have fully entered the Information Age, startling breakthroughs in information technology have irreversibly altered the ability to conduct business unconstrained by the traditional limitations of time or space. Today, it’s almost impossible to imagine a world without intranets, e-mail, and portable computers. With stunning speed, the Internet is profoundly changing the way we work, shop, do business, and communicate.As a consequence, we have truly entered the Post-Industrial economy. We are rapidly shifting from an economy based on manufacturing and commodities to one that places the greatest value on information, services, support, and distribution. That shift, in turn, place an unprecedented premium on “knowledge workers,” a new class of wealthy, educated, and mobile people who view themselves as free agents in a seller’s market.Beyond the realm of information technology, the accelerated pace of technological change in virtually every industry has created entirely new business, wiped out others, and produced a Pervasive (广泛的) demand for continuous innovation. New product, process, and distribution technologies provide powerful levers for creating competitive value. More companies are learning the importance of destructive technologies — innovations that hold the potential to make a product line, or even an entire business segment, virtually outdated.Another major trend has been the fragmentation of consumer and business markets. There’s a growing appreciation that superficially similar groups of customers may have very different preferences in terms of what they want to buy and how they want to buy it. Now, new technology makes it easier, faster, and cheaper to identify and serve targeted micro-markets in ways that were physically impossible or prohibitively expensive in the past. Moreover, the trend feeds on itself, a business’s abilit y to serve sub-markets fuels customers’ appetites for more and more specialized offerings.36.According to the first paragraph, the changes in the business environment in the past decades can be attributed to ________.A) technological advancesB) worldwide economic disorderC) the fierce competition in industryD) the globalization of economy正确答案：D37.What idea does the author want to convey in the second paragraph?A) The rapid development of information technology has taken businessmen by surprise.B) Information technology has removed the restrictions of time and space in business transactions.C) The Internet, intranets, e-mail, and portable computers have penetrated every corner of the world.D) The way we do business today has brought about startling breakthroughs in information technology.正确答案：B38.If a business wants to thrive in the Post-Industrial economy, ________.A) it has to invest more capital in the training of free agents to operate in a seller’s marketB) it should try its best to satisfy the increasing demands of mobile knowledgeable peopleC) it should not overlook the importance of information, services, support, and distributionD) it has to provide each of its employees with the latest information about the changing market正确答案：C39.In the author’s view, destructive technologies are innovations which ________.A) can eliminate an entire business segmentB) demand a radical change in providing servicesC) may destroy the potential of a company to make any profitD) call for continuous improvement in ways of doing business正确答案：A40.With the fragmentation of consumer and business markets ________.A) an increasing number of companies have disintegratedB) manufacturers must focus on one special product to remain competitive in the marketC) it is physically impossible and prohibitively expensive to do business in the old wayD) businesses have to meet individual customers’ specific needs in order to succeed正确答案：DPart III Vocabulary and Structure ( 10 minutes )Directions: There are a number of incomplete sentences in this part. For each sentence there are four choices marked A), B), C) and D). Choose the ONE that best completes the sentence.41.The police found no ________ of a terrorist link with the murder.A) proofsB) argumentsC) evidenceD) grounds正确答案：C42.As time goes by, his daughter is ________ beautiful.A) mostB) muchC) increasingD) increasingly正确答案：D43.The government has just drafted a law ________ foreign companies.A) virtuous toB) virtuous ofC) advantageous forD) advantageous to正确答案：D44.The lost car of the Lees was found _______ in the woods off the highway.A) vanishedB) abandonedC) scatteredD) rejected正确答案：B45.Expert say walking is one of the best ways for a person to _______ healthy.A) preserveB) stayC) maintainD) reserve正确答案：B46.The students expected there _______ more reviewing classes before the final exam.A) isB) beingC) have beenD) to be正确答案：D47.You can arrive in Beijing earlier for the meeting _______ you don't mind taking the night train.A) providedB) unlessC) thoughD) until正确答案：A48.There is no reason they should limit how much vitamin you take, _______ they can limit how much water you drink.A) much more thanB) no more thanC) no less thanD) any more than正确答案：D49.He was the only _____ of the plane crash.A) survivorB) personC) manD) crew正确答案：A50.His chief __________ is his winning smile.A) liabilityB) capitalC) assetD) accounts正确答案：C51.The topic ____________ on the crisis in these two countries.A) centersB) basisC) coreD) seats正确答案：A52.William once _____ that music was his life. Everything he has in life he owes to his music.A) hopedB) declaredC) desiredD) charged正确答案：B53.Once he decided what he wanted, he would _____ it with single-mindedness.A) go out ofB) go on withC) go ahead ofD) go after正确答案：D54.Seeing the old man crossing the road, _____ in time to prevent an accident.A) the driver came to a halt to the carB) the driver brought the car to a haltC) the driver made a halt to the carD) the driver called the car to a halt正确答案：B55.All flights _____ because of the storm, they decided to take the train.A) having canceledB) having been canceledC) were canceledD) have been canceled正确答案：B56.She read a poem __________ The Apple Tree.A) enabledB) labelledC) entitledD) authorized正确答案：C57.The __________ of that school took five years.A) establishmentB) organizationC) formationD) constitution正确答案：A58.It is known to all that little perseverance _____ between success and failure.A) makes no differenceB) makes little differenceC) makes a differenceD) makes all the difference正确答案：D59.The house has a pleasant __________ over the valley.A) outlookB) overlookC) lookoutD) view正确答案：A60.I didn’t want to __________ Mother’s misery.A) add toB) add up toC) odd toD) add正确答案：APart IV Translation ( 10 minutes )Directions: Complete the sentences by translating into English the Chinese given in brackets.61. We must ____________________ (达到平衡) between work and rest.正确答案：strike a balance62. It ____________________ (无所谓) if you are late to my party. I just want you to come.正确答案：makes no difference63. She doesn't even know how to boil potatoes, ____________________ (更别说为你准备晚餐了).正确答案：let alone prepare dinner for you64. Mary was laid off because ____________________ (她与上司不和).正确答案：she was at odds with her boss65. Young children may run around and make a lot of noise. Actually ____________________ (他们的行为与他们的年龄相符).正确答案：they are acting appropriately for their age。
外研版九年级上册教学工作总结（共13篇）
外研版九年级上册教学工作总结（共13篇）第1篇：外研版九年级上册教学计划九年级英语上册教学计划一、教学目标通过训练学生的听、说、读、写，使学生掌握最基本的语言知识和语言技能，从而培养学生初步运用英语进行交际的能力；寓教于乐，使学生养成良好的外语学习习惯，为将来的学习打下坚实的基础。
以教材为载体，密切结合教材，在课堂上努力创设各种情景夯实语言知识及语言技能，从而激发学生主动学习英语的兴趣，提高学生的记忆、观察、思维及想象能力，为学生的终身学习奠定基础。
二、学情分析我任教九年级一、二班英语。
从整体情况来看，一班学生普遍英语基础较差，兴趣不高，甚至有部分学生的听、说、读、写能力还不如小学五年级水平，所以在课堂教学时，出现有学生不守课堂规则，不愿听课、做与课堂无关事情的现象，难以形成英语学习氛围。
有部分学生基础较好，自制能力较强，能认真听课，按老师要求完成各项任务。
二班稍稍好一些，总的来说，这两个班的英语教学具有挑战性，需要耗费时间和精力。
三、教材分析九年级英语是外语教学与研究出版社出版的。
教材编排有以下目的：1、要使学生受到听、说、读、写、英语的训练，掌握最基础的语言知识和语言技能以及培养初步运用英语交际的能力；养成良好的外语学习习惯，掌握学习外语的基本方法；为进一步学习和运用英语打下扎实的基础。
2、使学生明确学习英语的目的性，3、培养初步运用英语交际的能力和自学能力。
教材内容：九年级英语上册，共十二模块，它包含了“状语从句，被动语态，定语从句”。
这些是让学生感到头痛的语法项目，也是初中阶段很重要的语法点。
四、教学措施与教学方法利用多媒体图文并茂、生动活泼地呈现教学内容，把语言学习和实际生活结合起来，增强学生的听说能力。
并通过开展各种任务性活动，巩固所学的知识。
鼓励学生通过思考、体验、参与、合作等方式来学习，增强学生独立思考的良好习惯以及口语表达和合作学习的能力；通过阅读训练，培养学生根据不同的阅读任务，运用适宜的阅读策略获取信息的本领，达到提高学生的英语理解能力和语言运用能力的目的。
南京大学20春《管理原理》第2次作业
C、organizational culture
D、manufacturing design
E、directing
说明：
题号:17题型:单选题（请在以下几个选项中选择唯一正确答案）本题分数:2
The three components that make up an attitude are ______________.
A、managers
B、leaders
C、organizers
D、visionaries
E、team members.
说明：
题号:6题型:单选题（请在以下几个选项中选择唯一正确答案）本题分数:2
Of the following, which is NOT a common source of information used by managers to measure performance?
A、measuring actual performance
B、changing the standard
C、taking managerial action
D、comparing actual against the standard
说明：
题号:11题型:单选题（请在以下几个选项中选择唯一正确答案）本题分数:2
A、cognitive, affective, behavioral.
B、traits, behavioral, emotional.
C、knowledge, opinion, individual history.
D、intention, opinion, environment.
E、pre-opinion, experience,
2020-2021学年石家庄第三中学高三英语下学期期末考试试卷及参考答案
2020-2021学年石家庄第三中学高三英语下学期期末考试试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ALook at Some Greatest BookstoresAnother CountryKreuzberg, Berlin, Germany. Another Country is an English Language second hand bookshop which is mostly used as a library. They have about 20, 000 books that you can buy or borrow. Some regular events are held at the shop, such as readings, cultural events, social evenings and film nights.Atlantis BooksOia, Santorini, Greece. Atlantis Books is an independent bookshop on the island of Santorini, Greece. It was founded in 2004 by a group of friends from Cyprus, England, and the United States. Throughout the year it has hosted literary festivals, film screenings, book readings, and good old fashioned dance parties.Bart’s BooksOjai, California. U. S. A. “The World’s Greatest Outdoor Bookstore”, a bookstore founded by Richard Bartinsdale in 1964. Shelves of books face the street, and regular customers are asked to drop coins into the door’s coin box to pay for any books they take whenever the store is closed.Adrian Harringtonsince 1971. Rare books: rare first editions; leather bound sets and general antiquarian(古玩).Address: 64a Kensington Church Street, Kensington, London, England, UK.Corso Como BookshopMilan, Italy. Extensive selection of publication on art architecture, design graphics and fashion, along with a strong emphasis on photography. It was founded in 1990 in Milan, Italy, by Carla Sozzamil.The BookwormChina. A bookshop, library, bar, restaurant and event space, now with four divisions in three cities — Beijing, Suzhou and Chengdu. The interconnecting rooms with floor-to-ceiling books on every wall are light and airy in summer, yet warm and comfortable in winter.1.What can you do in Atlantis Books?A.Enjoy rare books.B.Attend a festival.C.Learn photography.D.Buy books anytime.2.Which bookstore has the longest history?A.Adrian Harrington.B.Atlantis Books.C.Bart’s Books.D.Corso Como Bookshop.3.How is The Bookworm different from the others?A.It is used as a library.B.It focuses on photography.C.It hosts all sorts of activities.D.It has branches in different cities.BZaki was small for his twelve years, and he was angry being treated as a child. Farid, his older brother, had been looked upon as a man long before he was Zaki’s age. Every day Farid and the other young Bahraini men went out in their wooden boats to dive for oysters (牡蛎). Many times Zaki begged to go along, but Faridalways refused to let him.So every day Zaki would go to the shallow water to practice. His grandfather, a former diver, would watch him and advise him. All morning, Zaki would practice diving beneath the waves. Every afternoon, again and again he would go underwater and hold his breath. With each day’s practice, his diving improved and he could hold his breath a little while longer. Soon Zaki felt as much at home in the water as he did out of it.Zaki rose early one day. He wanted to compete with his brother. They dived beneath the waves. Zaki opened his eyes and found himself looking into his brother’s face. Farid was smiling with confidence. Slowly, the smile was disappearing from Farid’s face. As more seconds passed, a worried look appeared on Farid’s face. Farid was realizing that Zaki could possibly beat him. Looking into Farid’s eyes, Zaki suddenly understood what losing could mean to his brother. Never would the villagers allow him to live it down. He would be laughed at by losing to a little child. Almost without thinking, Zaki kicked his feet and rose to the surface of the water a second before Farid’s head appeared beside him.The men around them cheered and patted Farid on the back. Farid, however, put his arm around Zaki’s shoulders. “Today,” Farid announced, “we shall have a new diver among us.” Then quietly, for Zaki’s ears alone, he said “Thank you, my brother.” And Zaki knew that they both had learned that it takes more than strength to makea man.4. What is the second paragraph mainly about?A. Zaki’s grandfather was a good diver.B. Zaki liked staying at home every day.C. Zaki practised hard in the water daily.D. Zaki’s grandfather encouraged him to dive.5. Which of the following best describes Zaki according to paragraph 3?A. Considerate.B. Ambitious.C. Confident.D. Adventurous.6. What can we infer from the last sentence of the text?A. Farid beat his little brother easily.B. Zaki was as strong as his brother.C. Zaki regretted losing the competition.D. Both Farid and Zaki had grown up.7. What is the best title for the text?A. Farid’s PrideB. Zaki’s ChallengeC. Brothers’ CompetitionD. Grandfather’s AdviceCBob, a Burroughs junior high school football player, always had his mom cheering him on. He didn’t play exciting positions. He played as a linebacker(中后卫球员). Sadly, he often found himself at the bottom of the piles, where everyone would jump onto each other at the end of every play. Bob's mom realized it was hard for her son to hear her cheering. She hadto find a solution, but couldn't find one.Then one day the coach from the school team asked him if he wanted to join the team. Bob wasecstatic, because he was only a ninth grader. His mom was also excited, since she loved football and especially loved watching her son play. She kept considering a way for him to hear her. A cowbell! That was it. Now from the bottom of the piles Bob would hear his mom shaking her cowbell crazily, knowing she was there for him.Bob's team finally made it to the state championship game. What exciting time to play at Busch Stadium under the lights! This experience made Bob appreciate all the years that his mom had sacrificed everything to get him to practice every day, to wash his uniforms, and to never miss a game. He had to do something.On the night of the state championship game, the loudspeakers introduced Bob, and as he walked onto the field his mom shook the cowbell, hard. However, it didn’t sound right. She looked its inside, and found a note saying,”Thank you, Mom.” Bob had left her a note expressing his appreciation for always being with him, filling her heart with warmth.Finally Burroughs claimed the title of State Champion. While others were cheering and admiring the state championship cup, Bob' s mom clutched(紧握) her cowbell happily.Years later, Bob’s mom died. While digging through her belongings, he found the cowbell with the note. Bob took it to his mom's funeral and rang it, whispering, "Thank you, Mom.”8. What does the underlined word "ecstatic” mean in Paragraph 2?A. CuriousB. DisappointedC. AnxiousD. Delighted9. Why did Bob's mom want to get a cowbell?A. To amuse her cow.B. To teach her cowC. To attract his attention.D. To make him hear her10. What can be learned from Paragraph 3?A. Bob's mom devoted much time to himB. Bob was the best player in his teamC. Bob owed his success to his coachD. Bob's mom was a football player at college11. Why didn’t the cowbell sound as usual that night?A. The mother was very weak.B. Bob had put a note inside the bell.C. The weather became terrible suddenlyD. The bell had been broken deliberates.DOne billion people in the world are short of water. How can this problem be solved. Some suggestions have been to desalinate ocean water or to build enormous water pipelines from areas where water is abundant. (Suggestions such as these prove extremely expensive when they are actually used.) One possibility that scientists are considering is pulling icebergs from either the North Pole or the South Pole to parts of the world with a water shortage. Although many questions must be answered before such a project could be tried, moving icebergs seems a reasonable possibility in the future.Engineers, mathematicians, and glaciologists from a dozen countries have been considering the iceberg as a future source of water. Saudi Arabia is particularly interested in this project because it has a great water shortage. Scientists estimate that it would take 128 days to transport a large iceberg (about 1/2 square mile) to Saudi Arabia.Yet the iceberg would be completely melted by the 104th day. Therefore, insulation would be essential, but how to insulate the iceberg remains an unsolved problem.The problems in transporting an iceberg are numerous. The first problem is choosing the iceberg to pull. The icebergs that form in the North Pole are quite difficult to handle because of their shape. Only a small portion extends above the water — most of the iceberg is below the surface, which would make it difficult to pull. South Pole icebergs, on the other hand, are flat and float like table tops. Thus they would be much easier to move.How can a 200-million-ton iceberg be moved. No ship is strong enough to pull such enormous weight through the water. Perhaps several ships could be used. Attaching ropes to an iceberg this size is also an enormous problem. Engineers think that large nails or long metal rods could be driven into the ice. What would happen if the iceberg splits into several pieces during the pulling. Even if an iceberg with very few cracks were chosen, how could it be pulled through stormy waters. Furthermore, once the iceberg reached its destination, very few ports would be deep enough to store it.All of these problems must be solved before icebergs can become a reasonable source of water. Yet scientists estimate that it will be possible to transport them in the near future. Each year, enough icebergs form to supply the whole world with fresh water for a full year. In addition, icebergs are free and nonpolluting. As a solution to the world’s water problems, icebergs may be a workable possibility.12. What is a problem in transporting iceberg?A. The size of the iceberg.B. The colour of the iceberg.C. The salt in the iceberg.D. The movement of air and water.13. What is the author’ attitude towards transporting iceberg?A. Pessimistic.B. Objective.C. Optimistic.D. Unconcerned.14. What does the last paragraph mainly tell us?A. It is hard to use iceberg.B. Iceberg are a good choice.C. There are problems with iceberg.D. Man finds no other ways to solve water shortage.15. What can be a suitable title for the text?A. Shortage of water.B. Icebergs for water.C. Scientists and icebergs.D. Iceberg—scientists headache.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
新视野读写Book 4 Unit 2教案
Unit 2 Secrets to beautyText A The confusing pursuit of beautyText B Making the choice to be truly beautifulTeaching Objectives:This unit addresses the topic of beauty, focusing on physical beauty and its relationship to satisfaction and perfection of human life. Text A centers on the differences between women and men in terms of how they perceive physical beauty. Text B introduces a reading skill —identifying the topic sentence. After learning them, Ss should be able to1. talk about people’s pursu it of beauty2. fully understand the text3. apply the phrases and patterns4. master the skill of writing a comparison / contrast essay5. master the reading skill — identifying the topic sentence.Time allotment:1st period------ Pre-reading; While-reading (Para.1-2)2nd period------While-reading (Para.4-8；Part III); Language focus.3rd period------ After-reading: structure analysis and writing.4th period------ Additional reading: Reading skills; comprehend Text B.Teaching Procedures:Pre-reading Activities (15minutes)1. What are these products in the following pictures (Lipstick, Nail polish, Eye shadow, Mascara, Eyeliner, Powder foundation) used for?2. Are beauty products used by women only? What do men usually do with their physical looks?3. Appreciate the following sayings about beauty and then talk about your own understanding of beauty.•Beauty outside catches the eyes but the real beauty that lies within captures the heart. •External beauty disappears as you age but internal beauty is remembered even when you are long gone from this earth.While-reading Tasks (75minutes)1. Students guess the main idea of each paragraph on the basis of the detailed information got by skimming.1) What is the easiest way out when a man is asked by a woman to comment on her looks? And why? (Para. 2)2) Do men and women perceive their own looks in the same way? (Para. 3)3)Why do men and women view their looks so differently? (Para. 6)4)What are the differences between men and women in care for details in women’s appearance? (Paras. 9-10)5)What conclusion does the author draw after contrasting men and women on different points ? (Para. 11)2. Detailed study of the text.●Detailed learning of key vocabulary and useful patterns1) affix value to 认为…有价值如果你真正想要吸引顾客，你就必须十分重视自己店里所卖产品的质量。
Josef Berger
vorgelegt von Josef Berger am 11. Januar 2002
Erstgutachter: Zweitgutachter:
Prof. H. Osswald Prof. M. Wolff (Universit¨ at T¨ ubingen)
Tag des Rigorosums: 22.07.2002
2 The Orthogonal Projection from L2 W (µ, H) onto LA (µ, H) . . . . 39
The Stochastic Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 The Skorohod Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 The Malliavin Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Representation of Martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 The Clark Ocone Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Reference to Abstract Wiener Spaces . . . . . . . . . . . . . . . . . . . . . . . . .65 Appendix: an Internal Representation of the L´ evy Transformation of Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 73
【创新设计】2021届高考英语基础温习 增分策略阅读与理解 词义猜想题逻辑推理法 北师大版(1)
阅读与明白得(10) 词义猜想题(逻辑推理法)网络信息时期网络对人们来讲愈来愈重要，网上购物谈天等都是人们生活不可缺少的一部份，此话题也成了高考的重要话题之一，如2021安徽卷阅读明白得D篇就涉及到此话题。
美文赏析In this age of new media，where nearly everyone engages in some form of social media，how do you draw a line between your online identity and your professional persona(形象)?While most of your micro blogs(微博)updates may be harmless，voicing①an opinion on a micro blog related to your employer can lead you into hot water. In some cases，it can even get you fired.Last year, a famous Australian journalist，Catherine Deveny，was sacked by her newspaper.The Age，after she made a number of posts on her microblogging site.According to her editor，“The views she has expr essed recently on Twitter are not in keeping with the standards we set at The Age.”This incident set_off②a heated debate over the rights and responsibil ities of using social media as a form of personal expression.A few months earlier，an Australian politician was expelled③from his party after he made racist remarks about American President Barack Obama.Similarly，in the UK，politician Stuart MacLennan was also fired by Britain's governing Labor Party after making offensive comments about the opposition on his Twitter account.According to a report by Digital Media,8 percent of US companies admit to firing workers because of Facebook activities，while 48 percent of employers are screening(挑选)applicants using social media sites.What this means is that today，social media users must be highly cautious about their online activities and the comments they make online.As the divide be tween public and private becomes increasing difficult to distinguish，④people must think twice before posting a controversial⑤or critical remark. This is particularly the case when handling an employer's official website or social media account.InHungary，an employee of telecommunications giant，Vodafone，was fired after tweeting(发微博)，on the company's off icial Twitter page，a joke made by a competitor.【解题导语】此刻愈来愈多的网民利用网络来发表自己的观点，却不知稍不注意就会为自己带来祸端。
the standard model
Discrete linear objects in dimension n :the standard modelEric Andres *IRCOM-SIC,SP2MI,BP 30179,F-86962Futuroscope Cedex,FranceReceived 15May 2002;received in revised form 4September 2002;accepted 17October 2002AbstractA new analytical description model,called the standard model,for the discretization of Eu-clidean linear objects (point,m -flat,m -simplex)in dimension n is proposed.The objects are defined analytically by inequalities.This allows a global definition independent of the number of discrete points.A method is provided to compute the analytical description for a given lin-ear object.A discrete standard model has many properties in common with the supercover model from which it derives.However,contrary to supercover objects,a standard object does not have bubbles.A standard object is ðn À1Þ-connected,tunnel-free and bubble-free.The standard model is geometrically consistent.The standard model is well suited for modelling applications.Ó2003Elsevier Science (USA).All rights reserved.Keywords:Discrete geometry;Digitization;Dimension n ;Simplex;m -flat1.IntroductionWhen working in discrete geometry,aside from considering an object simply as a set of discrete points,the problem of defining discrete geometrical objects arises.A discrete 2D line segment can be defined as 8-connected,4-connected or even discon-nected as a dotted line.There is not a unique way of defining a discrete object or of digitizing a Euclidean object.This problem has been around for 40years and many different discrete object definitions have been proposed.One can say thatauthors Graphical Models 65(2003)92–111*Fax:+33-5-49-49-6570.E-mail address:andres@sic.univ-poitiers.fr.1524-0703/03/$-see front matter Ó2003Elsevier Science (USA).All rights reserved.doi:10.1016/S1524-0703(03)00004-3E.Andres/Graphical Models65(2003)92–11193 have followed three main approaches to define discrete geometrical objects:an algo-rithmic approach,a topological approach,and a more recent analytical approach followed in this paper.In the algorithmic approach[1,10,13,16,21–24,34]a discrete object is the result of a generation algorithm.Historically,thefirst approach that has been used,it has shown a number of limitations.It is often difficult to control the properties of the so defined discrete objects.For instance,the discrete objects might not be geometrically consistent:the edge of a3D triangle is typically not nec-essary a3D line segment or the3D triangle is not a piece of3D plane[21,22].It is also difficult to propose generation algorithms for discrete objects in dimension high-er than three.Except for n-dimensional lines[34],to the best authors knowledge,no discrete object,in dimensions higher than three,has been algorithmically defined.In the topological approach,a discrete object is typically defined as a class of objects verifying local properties,often topological in nature[18–20,25,28].While it is,by definition,easier to obtain the desired properties,it is difficult to be sure with such an approach,that the class of objects defined by a given set of properties is not larger than what is initially expected.A third,more recent approach,defines a discrete ob-ject by a global analytical definition[2–5,7,9,17,18,25,30,32].This approach has many advantages such as providing a compact definition(independent on the num-ber of points forming the discrete object),a global control of the discrete object.It has also an advantage that is not immediately visible when one is not familiar with this approach.It allows a good control of the local topological properties of the ob-ject.The many links with mathematical morphology are also an interesting property of some analytically defined models such as the supercover model[7,19,26,29,31,33]. One of the main advantages is that it is relatively easy to define discrete objects in an arbitrary dimension[3,4,7,30,32].The standard model introduced in the following pages is analytically defined.A new analytical description model for all linear objects in dimension n(discrete points,m-flats,and geometrical simplices)is presented in this paper.The analytical model is called the standard model.The names derives from the name given by Francßon[18]toðnÀ1Þ-connected analytical discrete3D planes(see also[4]for gen-eral details on discrete analytical hyperplanes).To the best authors knowledge,it is thefirst time that a discrete model is proposed that defines a large class of discrete objects in arbitrary dimensions.The standard model is called a discrete analytical model because the discrete objects(points,m-flats,simplices)are defined analytically by inequalities.The analytical definition is independent of the number of discrete points of the object.For instance,a3D standard triangle is defined by17or less in-equalities independently of its size.The model we propose has many interesting properties.The model is geometri-cally consistent:for instance,the vertices of a3D standard polygon are3D standard points,the edges of a3D standard polygon are3D standard line segments and the 3D standard polygon is a piece of a3D standard plane.It has been shown that the standard model is in fact a0-discretization of Brimkov et al.[12]and therefore isðnÀ1Þ-connected and tunnel-free.In3D,ðnÀ1Þ-connectivity in our notations corresponds to the classical6-connectivity.Contrary to the supercover model,from which it derives,the standard objects are bubble-free.One of the problems of the su-percover model is that it is not topologically consistent.A supercover m -flat is always ðn À1Þ-connected but sometimes it has simple points (located on so-called bubbles on the object).This makes the model difficult to use in practice [14,15].For instance,a supercover of a Euclidean n D point can be composed of any 2i discrete points,06i 6n .A standard m -flat is almost identical to the supercover m -flat,it remains ðn À1Þ-connected and tunnel-free,except for the simple points in the bubbles that are removed.The standard digitization of a n D Euclidean point is always composed only of one discrete point.Finally,the standard model has a very important property in the framework of discrete modelling:S t ðF [G Þ¼S t ðF Þ[S t ðG Þ.This means that,for instance,the definition of the standard 3D polygon is sufficient to define the standard model of an arbitrary Euclidean polygonal 3D object.The definition of the standard model is derived from the supercover model [2,5–7,14,15,31].A standard object is obtained by a simple rewriting process of the in-equalities defining analytically a supercover object [7].A supercover linear object is defined by a set of inequalities ‘‘P n i ¼1a i X i 6a 0.’’The simple points in the bubbles are points that verify ‘‘P n i ¼1a i X i ¼a 0.’’In order to remove the simple points,and thus bubbles,some of the inequalities need simply to be rewritten into ‘‘P n i ¼1a i X i <a 0.’’The selection of inequalities that are modified is based on an ori-entation convention.Depending on the orientation of the half-space,the corre-sponding inequality is modified or not.In Section 2,we introduce our notations and the principal properties of the super-cover model on which the standard model is based.In Section 3the standard model is introduced and defined.We start,in Section 3.1,by explaining why such a ‘‘heavy’’mathematical machinery is necessary to define ðn À1Þ-connected discrete objects.We show in particular why a classical,misleading,approach does not work.In Sec-tion 3.2,we explain the basic ideas behind the standard model.In Section 3.3,we introduce the orientation convention that forms the basis of the definition of the standard model.The standard model is defined for all linear primitives in dimension n in Section 3.4.The properties of the standard primitives,especially the tunnel-free-ness and the ðn À1Þ-connectivity,are presented in Section 3.5.In Section 4,we ex-amine the different classes of standard linear objects to see how the definition is translated in practice and how the different inequalities defining the objects are estab-lished.Conclusion and several perspectives are presented in Section 5.2.Preliminaries2.1.Basic notations in discrete geometryMost of the following notations correspond to those given by Cohen and Kauf-man in [14,15]and those given by Andres in [7].We provide only a short recall of these notions.Let Z n be the subset of the n D Euclidean space R n that consists of all the integer coordinate points.A discrete (resp.Euclidean )point is an element of Z n (resp.R n ).A discrete (resp.Euclidean )object is a set of discrete (resp.Euclidean )points.A discrete94 E.Andres /Graphical Models 65(2003)92–111inequality is an inequality with coefficients in R from which we retain only the integer coordinate solutions.A discrete analytical object is a discrete object defined by a fi-nite set of discrete inequalities .An m -flat is a Euclidean affine subspace of dimension m .Let us consider a set P of m þ1linearly independent Euclidean points P 0;...;P m .We denote A m ðP Þthe m -flat induced by P (i.e.,the m -flat containing P ).We denote S m ðP Þthe geometrical simplex of dimension m in R n induced by P (i.e.,the convex hull of P ).For S ¼S m ðP Þa geometrical simplex,we denote S ¼A m ðP Þthe corre-sponding m -flat.For an n -simplex S ¼S n ðP Þ,we denote E ðS ;P i Þthe half-space of boundary A n À1ðP n P i Þthat contains P i (see Fig.1).We denote p i the i th coordinate of a point or vector p .Two discrete points p and q are k -neighbours ,with 06k 6n ,if j p i Àq i j 61for 16i 6n ,and k 6n ÀP ni ¼1j p i Àq i j .The voxel V ðp Þ&R n of a discrete n D point p is definedby V ðp Þ¼½p 1À12;p 1þ12 ÂÁÁÁ½p n À12;p n þ12 .For a discrete object F ,V ðF Þ¼S p 2F V ðp Þ.We denote r n the set of all the permutations of f 1;...;n g .Let us de-note J nm the set of all the strictly growing sequences of m integers all between 1and n :J n m ¼f j 2Z m j 16j 1<j 2<ÁÁÁ<j m 6n g .This defines a set of multi-indices .Let us consider an object F in the n -dimensional Euclidean space R n ,with n >1.The orthogonal projection is defined by:p i ðF Þ¼fðq 1;...;q i À1;q i þ1;...;q n Þj q 2R n gfor 16i 6n ;p j ðF Þ¼ðp j 1 p j 2 ÁÁÁ p j m ÞðF Þfor j 2J n m :The orthogonal extrusion is defined bye j ðF Þ¼p À1j ðp j ðF ÞÞfor j 2J n m :Example.Let us consider the set of points P ¼f P 0ð0;0;0Þ;P 1ð9;1;1Þ;P 2ð3;8;4Þg .The corresponding simplex T ¼S 2ðP Þis a 3D triangle.The orthogonal projection p 2ðT Þ¼S 2ðp 2ðP ÞÞ¼S 2ðfð0;0Þ;ð9;1Þ;ð3;4ÞgÞis a 2D triangle.The orthogonal ex-trusion e 2ðT Þ¼fð0;t ;0Þ;ð9;t ;1Þ;ð3;t ;4Þj t 2R g is a 3D Euclidean object defined by threehalf-spaces.Fig.1.Triangle T ¼S 2ðf P 0;P 1;P 2gÞ,edge S 1ðf P 0;P 1gÞ,straight line A 1ðf P 0;P 1gÞ,and half-space E ðf P 0;P 1;P 2g ;P 2Þ.E.Andres /Graphical Models 65(2003)92–11195We define an axis arrangement application r j,for j2J nm,by: r j:R n!R nx!ðx rjð1Þ;x rjð2Þ;...;x rjðnÞÞ;where the permutation r j2r n is defined byr j¼for16i6m;r jðj iÞ¼i else for m<i6n;r jðk rÞ¼iso that k r<k rþ1and k r¼j s for all16r6nÀm and for all16s6m.The axis arrangement application has been specifically designed so that it verifies the twofollowing properties:p jðFÞ¼pð1;2;...;mÞðrÀ1j ðFÞÞand e jðFÞ¼r jðeð1;2;...;mÞðrÀ1jðFÞÞÞfor allF in R n and j2J nm.Example.Let us consider the5D point Pð1;2;3;4;5Þand j¼ð2;4Þ2J52.Thecorresponding axis arrangement application is defined by rð2;4Þ:x!ðx3;x1;x4;x2;x5Þand rÀ1ð2;4Þ:x!ðx2;x4;x1;x3;x5Þ.The orthogonal projection verifies pð2;4ÞðPÞ¼pð1;2ÞðrÀ1ð2;4ÞðPÞÞ¼pð1;2Þð2;4;1;3;5Þ¼ð1;3;5Þ.The orthogonal extrusion verifies eð2;4Þð1;3;5Þ¼rð2;4Þðeð1;2ÞðrÀ1ð2;4ÞðPÞÞÞ¼rð2;4Þðeð1;2Þð2;4;1;3;5ÞÞ¼rð2;4ÞðpÀ1ð1;2Þð1;3;5ÞÞand therefore eð2;4Þð1;3;5Þ¼rð2;4Þðfðt;u;1;3;5Þjðt;uÞ2R2gÞ¼fð1;t;3;u;5Þjðt;uÞ2R2g.2.2.Geometric properties of the supercoverA discrete object G is a cover of a Euclidean object F if F&VðGÞand 8p2G;VðpÞ\F¼£.The supercover SðFÞof a Euclidean object F is defined by SðFÞ¼f p2Z n j VðpÞ\F¼£g(see Fig.2a).SðFÞis by definition a cover of F.It is easy to see that if G is a cover of F,then G&SðFÞ.The supercover of FcanFig.2.Supercover definitions.96 E.Andres/Graphical Models65(2003)92–111be defined in different ways:S ðF Þ¼ðF ÈB 1ð12ÞÞ\Z n ¼f p 2Z n j d 1ðp ;F Þ612g (see Fig.2b)where B 1ðr Þif the ball centered on the origin,of radius r for the distance d 1.This links the supercover to mathematical morphology [7,26,29,31].The supercover has many properties.Let us consider two Euclidean objects F andG ,and a multi-index j 2J n m ,then:S ðF Þ¼S a 2F S ða Þ,S ðF [G Þ¼S ðF Þ[S ðG Þ,ifF &G ,then S ðF Þ&S ðG Þ.These properties are well known [14,15].The following properties are more recent and are useful in the framework of this paper:S ðF ÂG Þ¼S ðF ÞÂS ðG Þ,r j ðS ðF ÞÞ¼S ðr j ðF ÞÞ,p j ðS ðF ÞÞ¼S ðp j ðF ÞÞ,and e j ðS ðF ÞÞ¼S ðe j ðF ÞÞ¼r j ðZ m ÂS ðp j ðF ÞÞÞ[7].Definition 1(Bubble ).A k -bubble,with 16k 6n ,is the supercover of a Euclidean point that has exactly k half-integer coordinates.A half-integer is a real l þ12,with l an integer.A k -bubble is formed of 2k discrete points.A 2-bubble can be seen in Fig.2a (marked by the black circle).The two white dots are what we call here ‘‘simple’’points.This corresponds to an extension of the notion of simple points that fits a supercover simplex.A point P belonging to the supercover simplex S is said to be a simple point if it is a simple point for S with the classical definition given in Section 2.1.Definition 2(Bubble-free ).The cover of an m -flat is said to be bubble-free if it has no k -bubbles for k >m .The cover of a simplex S is said to be bubble-free if S is bubble-free.There are two types of bubbles in the supercover of an m -flat F .The k -bub-bles,for k 6m ,are discrete points that are part of all the covers of F .If we remove any of these points,the discrete object is not a cover anymore.In the k -bubbles,for k >m ,there are discrete points that are ‘‘simple’’points.The aim of this paper is to propose discrete analytical objects that are bubble-free and ðn À1Þ-connected by removing some of the simple points.In Fig.2a,by removing one of the two simple points,we obtain a bubble-free,1-connected discrete 2D line segment.Lemma 1.A discrete point p belongs to a k -bubble,k >m ,of the supercover of an m -flat F if and only if there exists a point a 2F with k half-integer coordinates such that p 2S ða Þ.The proof of this lemma is obvious.3.Standard modelThe aim of this paper is to propose a new cover class,called the standard cover.The standard cover is so far only defined for linear objects in all dimensions.The dis-crete analytical model has been designed to conserve most of the properties of theE.Andres /Graphical Models 65(2003)92–11197supercover,to be bubble-free andðnÀ1Þ-connected.The supercover model has al-most all the properties we are looking for:tunnel-freeness,ðnÀ1Þ-connectivity,sta-bility for union,etc.The only property that is missing is the bubble-freeness.Some supercover objects have simple points.The model is therefore not topologically con-sistent and this is a problem for several applications such as,for instance,polygonal-ization.For this reason several attempts have been made to modify the supercover discretization by modifying the definition of a pixel[14,15,27].We show in the fol-lowing section that such attempts cannot work.In our approach,presented in Sec-tion3.2,we explain how,by studying the analytical description of linear objects,it is possible to remove selectively the simple points in the supercover model while pre-serving the modeling properties.In the section that follow the standard model and its properties are introduced.3.1.What does not work with the classical approachSeveral unsuccessful attempts have been made to define discrete objects that have supercover type modeling properties with bubble-freeness andðnÀ1Þ-connectivity properties[14,15,27].All these ideas basically modify,in various ways,the definition of a voxel in order to avoid bubbles.We give here a simple such example and show why it does not work that way(see[14]for some other examples).In Fig.3,the pixel definition has been changed.A pixel is now formed of the SW vertex(black disk),the two corresponding edges(bold edges)and itsÕinterior.The three other vertices and two other edges do not belong to the pixel.This definition derives thatSp2Z n VðpÞ¼R n with VðpÞ\VðqÞ¼£for p¼q:The discretization of a discreteline is necessarily bubble-free.However,as we see in Fig.3,the discretised line x1Àx2¼0is not1-connected.In fact,it has been shown as early as in1970[27],that no change in the definition of the pixel or voxel can lead to a correct solution.This means that a simple pixel definition modification avoids bubbles but creates primi-tives that are not topologically consistent.This makes such a model useless for ap-plications such as polygonalization.Tunnel-freeness property is also lost with such an approach.3.2.Standard model approach:a modification of the supercover definitionThe discrete analytical description of the supercover of a linear convex is defined as intersection of half-spaces defined by discrete inequalities P n i ¼1a i x i 6a 0[2,5–7].A linear concave object is simply considered as union of convexes.The orientation of each half-space is checked with an orientation convention and depending on it,its inequality ‘‘P n i ¼1a i x i 6a 0’’remains unchanged or is replaced by ‘‘P n i ¼1a i x i <a 0.’’Let us give a simple example,the 2D straight line D :3x 1À7x 2¼0shown in Fig.4,to illustrate why and how this works.The general case in dimension n works ex-actly in the same way.The supercover of the Euclidean line D is described by the two inequalities S ðD Þ¼fðx 1;x 2Þ2Z 2j À563x 1À7x 265g .A bubble occurs only when the straight line D contains half-integer coordinate points.We have then (and only then)discrete points verifying on one side 3x 1À7x 2¼À5and on the other side 3x 1À7x 2¼5.All these points are simple points.Removing the points on one side only leads to a discrete straight line that is 1-connected,separating,1-minimal and bubble-free.This can be done simply by replacing a ‘‘6’’by a ‘‘<’’for one of the two inequalities in the supercover analytical description.In the case of Fig.4,we have S t ðD Þ¼fðx 1;x 2Þ2Z 2j À563x 1À7x 2<5g .The change is based on an orien-tation convention.Opposing half-spaces such as ‘‘3x 1À7x 265’’and ‘‘À3x 1þ7x 265’’have a different orientation in this convention and thus only one of them will have its Õ‘‘6’’changed into ‘‘<.’’This ensures that only one simple point for the 2D line will be removed.3.3.Orientation conventionThe standard model,contrary to the supercover,is not unique [7,9].For instance,in example of Fig.4,one of two possible simple points can be removed.Each selec-tion leads to another standard model definition.It depends on the orientation con-vention selection.One orientation convention per dimension R m ,m >0,isrequired.Fig.4.Standard and supercover straight line.The black points belong to both line.The white point be-longs only to the supercover.E.Andres /Graphical Models 65(2003)92–11199This selection must then remain unchanged for all the primitives handled.The selec-tion of an orientation convention per dimension has to be coherent with the operator p .The property S t ðp j ðF ÞÞ¼p j ðS t ðF ÞÞfor the operator p should be verified.If this is not the case,the modelling properties would not be verified (such as S t ðF [G Þ¼S t ðF Þ[S t ðG Þ,etc.).In general,with arbitrary orientation conventions there is no reason for this property to be verified.We propose a set of orientation conventions,denoted O n and called the basic orientation conventions.The basic ori-entation conventions verify the above mentioned property.Definition 3(Standard orientation ).Let us consider a discrete analytical half-space E :P n i ¼1C i X i 6B and the basic orientation convention O n .We say that E has a standard orientation if:•C 1>0;•or if C 1¼0and C 2>0;•...•or if C 1¼ÁÁÁ¼C n À1¼0and C n >0:If E has not a standard orientation,then we say that E has a supercover orientation.We consider from now on,without loss of generality,only the basic orientation conventions for all n >0.All the standard primitives are defined with these basic ori-entation conventions.The basic orientation conventions are coherent with respect to the operators p .After p j ,for j 2J nm ,the orientation convention O n in R n becomesO n Àm in R n Àm .3.4.Standard model definitionAll the elements required to define the standard discretization model of linear ob-jects in R n are available.Definition 4(Standard model ).Let F be a linear Euclidean object in R n whose su-percover is described analytically by a finite set of inequalities F k :P n i ¼1C i ;k X i 6B k .The standard model S t ðF Þof F ,for the basic orientation convention O n ,is the discrete object described analytically by a finite set of discrete inequalities F 0k ob-tained by substituting each inequality F k by F 0k defined as follows:•If F k has a standard orientation,then F 0k :P n i ¼1C i ;k X i <B k ;•else F 0k :P n i ¼1C i ;k X i 6B k .This definition is algorithmically easy to set up.Once a discrete analytical descrip-tion of an object is available,the transition from the supercover model to the stan-dard model and vice versa is trivial.3.5.Geometric properties of the standard modelIn this section,some properties of the standard model are presented.These prop-erties are very important for the derivation of our model description.Let us consider100 E.Andres /Graphical Models 65(2003)92–111a Euclidean linear object F of topological dimension m in R n .We have by definition S t ðF Þ&S ðF Þeven more precisely,if p 2S ðF Þn S t ðF Þ,then d 1ðp ;F Þ¼12.A stan-dard object is a supercover object from which some discrete points have been re-moved.These points are all at a distance 1from the Euclidean primitive.We have S t ðF Þ¼S ðF Þif no point,with at least m þ1half-integer coordinates,belongs to the boundary of F .The differences between the supercover of F and the standard model of F are located in the k -bubbles of F ,for k >m .Fig.4illustrates this in di-mension 2.One of the immediate consequences of this last property,is that the stan-dard model remains a cover:F &V ðS t ðF ÞÞ.That is why the standard model is also sometimes called standard cover [33,31].The standard model retains most of the set properties of the supercover.It is easy to deduce from Definition 4,that if we consider two Euclidean linear objects F and G in R n ,then:S t ðF [G Þ¼S t ðF Þ[S t ðG Þ;S t ðF \G Þ&S t ðF Þ\S t ðG Þ;F &G )S t ðF Þ&S t ðG Þ;S t ðF ÂG Þ¼S t ðF ÞÂS t ðG Þ;S t ðp j ðF ÞÞ¼p j ðS t ðF ÞÞ;S t ðe j ðF ÞÞ¼e j ðS t ðF ÞÞ:The first property ensures that we will be able to construct complex discrete ob-jects out of basic elements such as simplices.These last properties are characteristic of correct orientation conventions.The properties are only verified if the orientation conventions are defined for all dimensions lower or equal to n and if they are coher-ent with respect to the operator p .This is the case for the basic orientation conven-tions O k ,for k 6n .It is important to notice that,in general,S t ðF Þ¼S a 2F S t ða Þ.This property of the supercover is not conserved.We have S t ðF [G Þ¼S t ðF Þ[S t ðG Þfor a union of a finite number of objects.This comes simply from the fact that the standard model is not defined for an analytical description that has an infinite number of discrete in-equalities.One simple example for that is given by the 2D line D :x 1Àx 2¼0:The standard model of the line is S t ðD Þ:À16x 1Àx 2<1while S a 2F S t ða Þ:À1<x 1Àx 2<1.One of the main properties of the standard model concerns the connectivity and the tunnel-freeness.Theorem 2(Connectivity and tunnel-freeness).Let F be a Euclidean linear object of topological dimension m in R n .Its standard model S t ðF Þis ðn À1Þ-connected and tunnel-free.The standard model is a particular case of k -discretizations as introduced by Brim-kov et al.in [12].It is shown that the standard model is in fact a 0-discretization (The-orem 3in [12])and that 0-discretizations are ðn À1Þ-connected and tunnel-free E.Andres /Graphical Models 65(2003)92–111101(Proposition 3in [11]and Theorem 4in [12]).Another property proved in [12,31,33]is that the standard model minimizes the Hausdorffdistance with the Euclidean object.4.Des cription ofs tandard primitivesWe will examine now the discrete analytical description of the different classes of standard linear primitives (half-space,point,m -flat and m -simplex)and how they can be computed.Our purpose here is to propose a discretization scheme that can be used in practical applications.As stated in Definition 4,every analytical description of a standard linear primitive is based on the analytical description of a standard half-space.That is the one we present first.We deduce from it the discrete analytical for-mulas describing a standard point,m -flat and m -simplex in the sections that follow.4.1.Standard half-spaceThe standard half-space is given by:Proposition 3(Standard half-space).Let us consider a Euclidean half-space E :P n i ¼1C i X i 6B .The standard model S t ðE Þof E ,according to an orientation convention,isanalytically described by:•If E has a standard orientation,then S t ðE Þ¼p 2Z n X n i ¼1C i p i (<B þP n i ¼1j C i j 2);•elseS t ðE Þ¼p 2Z n X n i ¼1C i p i (6B þP n i ¼1j C i j 2):The proposition is an immediate extension to dimension n of results on the super-cover [2,4,5,7]and of Definition 4.4.2.Standard pointThe analytical description of a standard point can easily be deduced from the one of the standard half-space.It is however interesting to notice that the standard dis-cretization of a Euclidean point is always composed of one and only one discrete point contrary to what happens with a supercover discretization of a Euclidean point that can be formed of 2k points,06k 6n (in case of a k -bubble).Proposition 4(Standard point).Let us consider a Euclidean point a 2R n and the basic orientation convention O n .The standard model S t ða Þof a is the discrete point102 E.Andres /Graphical Models 65(2003)92–111。